diff --git a/dist/3.x/mat3-impl.d.ts b/dist/3.x/mat3-impl.d.ts index b3d28b7..1f7eeee 100644 --- a/dist/3.x/mat3-impl.d.ts +++ b/dist/3.x/mat3-impl.d.ts @@ -30,8 +30,18 @@ export declare function getAPI(Ctor: Mat3Ctor< translate: (m: BaseArgType, v: BaseArgType, dst?: T_17 | undefined) => T_17; rotation: (angleInRadians: number, dst?: T_18 | undefined) => T_18; rotate: (m: BaseArgType, angleInRadians: number, dst?: T_19 | undefined) => T_19; - scaling: (v: BaseArgType, dst?: T_20 | undefined) => T_20; - scale: (m: BaseArgType, v: BaseArgType, dst?: T_21 | undefined) => T_21; - uniformScaling: (s: number, dst?: T_22 | undefined) => T_22; - uniformScale: (m: BaseArgType, s: number, dst?: T_23 | undefined) => T_23; + rotationX: (angleInRadians: number, dst?: T_20 | undefined) => T_20; + rotateX: (m: BaseArgType, angleInRadians: number, dst?: T_21 | undefined) => T_21; + rotationY: (angleInRadians: number, dst?: T_22 | undefined) => T_22; + rotateY: (m: BaseArgType, angleInRadians: number, dst?: T_23 | undefined) => T_23; + rotationZ: (angleInRadians: number, dst?: T_18 | undefined) => T_18; + rotateZ: (m: BaseArgType, angleInRadians: number, dst?: T_19 | undefined) => T_19; + scaling: (v: BaseArgType, dst?: T_24 | undefined) => T_24; + scale: (m: BaseArgType, v: BaseArgType, dst?: T_25 | undefined) => T_25; + uniformScaling: (s: number, dst?: T_26 | undefined) => T_26; + uniformScale: (m: BaseArgType, s: number, dst?: T_27 | undefined) => T_27; + scaling3D: (v: BaseArgType, dst?: T_28 | undefined) => T_28; + scale3D: (m: BaseArgType, v: BaseArgType, dst?: T_29 | undefined) => T_29; + uniformScaling3D: (s: number, dst?: T_30 | undefined) => T_30; + uniformScale3D: (m: BaseArgType, s: number, dst?: T_31 | undefined) => T_31; }; diff --git a/dist/3.x/wgpu-matrix.d.ts b/dist/3.x/wgpu-matrix.d.ts index 5e6bafe..4f2b74d 100644 --- a/dist/3.x/wgpu-matrix.d.ts +++ b/dist/3.x/wgpu-matrix.d.ts @@ -62,10 +62,20 @@ mat3: { translate: (m: BaseArgType, v: BaseArgType, dst?: T_16 | undefined) => T_16; rotation: (angleInRadians: number, dst?: T_17 | undefined) => T_17; rotate: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; - scaling: (v: BaseArgType, dst?: T_19 | undefined) => T_19; - scale: (m: BaseArgType, v: BaseArgType, dst?: T_20 | undefined) => T_20; - uniformScaling: (s: number, dst?: T_21 | undefined) => T_21; - uniformScale: (m: BaseArgType, s: number, dst?: T_22 | undefined) => T_22; + rotationX: (angleInRadians: number, dst?: T_19 | undefined) => T_19; + rotateX: (m: BaseArgType, angleInRadians: number, dst?: T_20 | undefined) => T_20; + rotationY: (angleInRadians: number, dst?: T_21 | undefined) => T_21; + rotateY: (m: BaseArgType, angleInRadians: number, dst?: T_22 | undefined) => T_22; + rotationZ: (angleInRadians: number, dst?: T_17 | undefined) => T_17; + rotateZ: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; + scaling: (v: BaseArgType, dst?: T_23 | undefined) => T_23; + scale: (m: BaseArgType, v: BaseArgType, dst?: T_24 | undefined) => T_24; + uniformScaling: (s: number, dst?: T_25 | undefined) => T_25; + uniformScale: (m: BaseArgType, s: number, dst?: T_26 | undefined) => T_26; + scaling3D: (v: BaseArgType, dst?: T_27 | undefined) => T_27; + scale3D: (m: BaseArgType, v: BaseArgType, dst?: T_28 | undefined) => T_28; + uniformScaling3D: (s: number, dst?: T_29 | undefined) => T_29; + uniformScale3D: (m: BaseArgType, s: number, dst?: T_30 | undefined) => T_30; }, /** * 4x4 Matrix functions that default to returning `Float32Array` @@ -357,10 +367,20 @@ export declare const mat3d: { translate: (m: BaseArgType, v: BaseArgType, dst?: T_16 | undefined) => T_16; rotation: (angleInRadians: number, dst?: T_17 | undefined) => T_17; rotate: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; - scaling: (v: BaseArgType, dst?: T_19 | undefined) => T_19; - scale: (m: BaseArgType, v: BaseArgType, dst?: T_20 | undefined) => T_20; - uniformScaling: (s: number, dst?: T_21 | undefined) => T_21; - uniformScale: (m: BaseArgType, s: number, dst?: T_22 | undefined) => T_22; + rotationX: (angleInRadians: number, dst?: T_19 | undefined) => T_19; + rotateX: (m: BaseArgType, angleInRadians: number, dst?: T_20 | undefined) => T_20; + rotationY: (angleInRadians: number, dst?: T_21 | undefined) => T_21; + rotateY: (m: BaseArgType, angleInRadians: number, dst?: T_22 | undefined) => T_22; + rotationZ: (angleInRadians: number, dst?: T_17 | undefined) => T_17; + rotateZ: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; + scaling: (v: BaseArgType, dst?: T_23 | undefined) => T_23; + scale: (m: BaseArgType, v: BaseArgType, dst?: T_24 | undefined) => T_24; + uniformScaling: (s: number, dst?: T_25 | undefined) => T_25; + uniformScale: (m: BaseArgType, s: number, dst?: T_26 | undefined) => T_26; + scaling3D: (v: BaseArgType, dst?: T_27 | undefined) => T_27; + scale3D: (m: BaseArgType, v: BaseArgType, dst?: T_28 | undefined) => T_28; + uniformScaling3D: (s: number, dst?: T_29 | undefined) => T_29; + uniformScale3D: (m: BaseArgType, s: number, dst?: T_30 | undefined) => T_30; }, mat4d: { create: (v0?: number | undefined, v1?: number | undefined, v2?: number | undefined, v3?: number | undefined, v4?: number | undefined, v5?: number | undefined, v6?: number | undefined, v7?: number | undefined, v8?: number | undefined, v9?: number | undefined, v10?: number | undefined, v11?: number | undefined, v12?: number | undefined, v13?: number | undefined, v14?: number | undefined, v15?: number | undefined) => Float64Array; set: (v0: number, v1: number, v2: number, v3: number, v4: number, v5: number, v6: number, v7: number, v8: number, v9: number, v10: number, v11: number, v12: number, v13: number, v14: number, v15: number, dst?: T | undefined) => T; @@ -627,10 +647,20 @@ export declare const mat3n: { translate: (m: BaseArgType, v: BaseArgType, dst?: T_16 | undefined) => T_16; rotation: (angleInRadians: number, dst?: T_17 | undefined) => T_17; rotate: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; - scaling: (v: BaseArgType, dst?: T_19 | undefined) => T_19; - scale: (m: BaseArgType, v: BaseArgType, dst?: T_20 | undefined) => T_20; - uniformScaling: (s: number, dst?: T_21 | undefined) => T_21; - uniformScale: (m: BaseArgType, s: number, dst?: T_22 | undefined) => T_22; + rotationX: (angleInRadians: number, dst?: T_19 | undefined) => T_19; + rotateX: (m: BaseArgType, angleInRadians: number, dst?: T_20 | undefined) => T_20; + rotationY: (angleInRadians: number, dst?: T_21 | undefined) => T_21; + rotateY: (m: BaseArgType, angleInRadians: number, dst?: T_22 | undefined) => T_22; + rotationZ: (angleInRadians: number, dst?: T_17 | undefined) => T_17; + rotateZ: (m: BaseArgType, angleInRadians: number, dst?: T_18 | undefined) => T_18; + scaling: (v: BaseArgType, dst?: T_23 | undefined) => T_23; + scale: (m: BaseArgType, v: BaseArgType, dst?: T_24 | undefined) => T_24; + uniformScaling: (s: number, dst?: T_25 | undefined) => T_25; + uniformScale: (m: BaseArgType, s: number, dst?: T_26 | undefined) => T_26; + scaling3D: (v: BaseArgType, dst?: T_27 | undefined) => T_27; + scale3D: (m: BaseArgType, v: BaseArgType, dst?: T_28 | undefined) => T_28; + uniformScaling3D: (s: number, dst?: T_29 | undefined) => T_29; + uniformScale3D: (m: BaseArgType, s: number, dst?: T_30 | undefined) => T_30; }, mat4n: { create: (v0?: number | undefined, v1?: number | undefined, v2?: number | undefined, v3?: number | undefined, v4?: number | undefined, v5?: number | undefined, v6?: number | undefined, v7?: number | undefined, v8?: number | undefined, v9?: number | undefined, v10?: number | undefined, v11?: number | undefined, v12?: number | undefined, v13?: number | undefined, v14?: number | undefined, v15?: number | undefined) => number[]; set: (v0: number, v1: number, v2: number, v3: number, v4: number, v5: number, v6: number, v7: number, v8: number, v9: number, v10: number, v11: number, v12: number, v13: number, v14: number, v15: number, dst?: T | undefined) => T; diff --git a/dist/3.x/wgpu-matrix.js b/dist/3.x/wgpu-matrix.js index b05791c..6d847f3 100644 --- a/dist/3.x/wgpu-matrix.js +++ b/dist/3.x/wgpu-matrix.js @@ -1,4 +1,4 @@ -/* wgpu-matrix@3.1.0, license MIT */ +/* wgpu-matrix@3.2.0, license MIT */ (function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) : typeof define === 'function' && define.amd ? define(['exports'], factory) : @@ -2319,9 +2319,129 @@ } return newDst; } + /** + * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + function rotationX(angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = 1; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = c; + newDst[6] = s; + newDst[8] = 0; + newDst[9] = -s; + newDst[10] = c; + return newDst; + } + /** + * Rotates the given 3-by-3 matrix around the x-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + function rotateX(m, angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const m10 = m[4]; + const m11 = m[5]; + const m12 = m[6]; + const m20 = m[8]; + const m21 = m[9]; + const m22 = m[10]; + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[4] = c * m10 + s * m20; + newDst[5] = c * m11 + s * m21; + newDst[6] = c * m12 + s * m22; + newDst[8] = c * m20 - s * m10; + newDst[9] = c * m21 - s * m11; + newDst[10] = c * m22 - s * m12; + if (m !== newDst) { + newDst[0] = m[0]; + newDst[1] = m[1]; + newDst[2] = m[2]; + } + return newDst; + } + /** + * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + function rotationY(angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = c; + newDst[1] = 0; + newDst[2] = -s; + newDst[4] = 0; + newDst[5] = 1; + newDst[6] = 0; + newDst[8] = s; + newDst[9] = 0; + newDst[10] = c; + return newDst; + } + /** + * Rotates the given 3-by-3 matrix around the y-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + function rotateY(m, angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const m00 = m[0 * 4 + 0]; + const m01 = m[0 * 4 + 1]; + const m02 = m[0 * 4 + 2]; + const m20 = m[2 * 4 + 0]; + const m21 = m[2 * 4 + 1]; + const m22 = m[2 * 4 + 2]; + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = c * m00 - s * m20; + newDst[1] = c * m01 - s * m21; + newDst[2] = c * m02 - s * m22; + newDst[8] = c * m20 + s * m00; + newDst[9] = c * m21 + s * m01; + newDst[10] = c * m22 + s * m02; + if (m !== newDst) { + newDst[4] = m[4]; + newDst[5] = m[5]; + newDst[6] = m[6]; + } + return newDst; + } + /** + * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + const rotationZ = rotation; + /** + * Rotates the given 3-by-3 matrix around the z-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + const rotateZ = rotate; /** * Creates a 3-by-3 matrix which scales in each dimension by an amount given by - * the corresponding entry in the given vector; assumes the vector has three + * the corresponding entry in the given vector; assumes the vector has two * entries. * @param v - A vector of * 2 entries specifying the factor by which to scale in each dimension. @@ -2344,7 +2464,7 @@ /** * Scales the given 3-by-3 matrix in each dimension by an amount * given by the corresponding entry in the given vector; assumes the vector has - * three entries. + * two entries. * @param m - The matrix to be modified. * @param v - A vector of 2 entries specifying the * factor by which to scale in each dimension. @@ -2369,7 +2489,55 @@ return newDst; } /** - * Creates a 3-by-3 matrix which scales uniformly in each dimension + * Creates a 3-by-3 matrix which scales in each dimension by an amount given by + * the corresponding entry in the given vector; assumes the vector has three + * entries. + * @param v - A vector of + * 3 entries specifying the factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ + function scaling3D(v, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = v[0]; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = v[1]; + newDst[6] = 0; + newDst[8] = 0; + newDst[9] = 0; + newDst[10] = v[2]; + return newDst; + } + /** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given by the corresponding entry in the given vector; assumes the vector has + * three entries. + * @param m - The matrix to be modified. + * @param v - A vector of 3 entries specifying the + * factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ + function scale3D(m, v, dst) { + const newDst = (dst ?? new Ctor(12)); + const v0 = v[0]; + const v1 = v[1]; + const v2 = v[2]; + newDst[0] = v0 * m[0 * 4 + 0]; + newDst[1] = v0 * m[0 * 4 + 1]; + newDst[2] = v0 * m[0 * 4 + 2]; + newDst[4] = v1 * m[1 * 4 + 0]; + newDst[5] = v1 * m[1 * 4 + 1]; + newDst[6] = v1 * m[1 * 4 + 2]; + newDst[8] = v2 * m[2 * 4 + 0]; + newDst[9] = v2 * m[2 * 4 + 1]; + newDst[10] = v2 * m[2 * 4 + 2]; + return newDst; + } + /** + * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions * @param s - Amount to scale * @param dst - matrix to hold result. If not passed a new one is created. * @returns The scaling matrix. @@ -2388,7 +2556,7 @@ return newDst; } /** - * Scales the given 3-by-3 matrix in each dimension by an amount + * Scales the given 3-by-3 matrix in the X and Y dimension by an amount * given. * @param m - The matrix to be modified. * @param s - Amount to scale. @@ -2410,6 +2578,46 @@ } return newDst; } + /** + * Creates a 3-by-3 matrix which scales uniformly in each dimension + * @param s - Amount to scale + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ + function uniformScaling3D(s, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = s; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = s; + newDst[6] = 0; + newDst[8] = 0; + newDst[9] = 0; + newDst[10] = s; + return newDst; + } + /** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given. + * @param m - The matrix to be modified. + * @param s - Amount to scale. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ + function uniformScale3D(m, s, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = s * m[0 * 4 + 0]; + newDst[1] = s * m[0 * 4 + 1]; + newDst[2] = s * m[0 * 4 + 2]; + newDst[4] = s * m[1 * 4 + 0]; + newDst[5] = s * m[1 * 4 + 1]; + newDst[6] = s * m[1 * 4 + 2]; + newDst[8] = s * m[2 * 4 + 0]; + newDst[9] = s * m[2 * 4 + 1]; + newDst[10] = s * m[2 * 4 + 2]; + return newDst; + } return { clone, create, @@ -2437,10 +2645,20 @@ translate, rotation, rotate, + rotationX, + rotateX, + rotationY, + rotateY, + rotationZ, + rotateZ, scaling, scale, uniformScaling, uniformScale, + scaling3D, + scale3D, + uniformScaling3D, + uniformScale3D, }; } const cache$3 = new Map(); diff --git a/dist/3.x/wgpu-matrix.js.map b/dist/3.x/wgpu-matrix.js.map index 8d5f7ce..f80671b 100644 --- a/dist/3.x/wgpu-matrix.js.map +++ b/dist/3.x/wgpu-matrix.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","/**\n * Some docs\n * @namespace wgpu-matrix\n */\nimport {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat3 */\n mat3: getMat3API(Mat3Ctor),\n /** @namespace mat4 */\n mat4: getMat4API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nconst rotationZ = rotation;\n\n/**\n * Rotates the given 3-by-3 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotateZ = rotate;\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has two\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * two entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 3 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling3D(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2];\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 3 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale3D(m: Mat3Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in the X and Y dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling3D(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale3D(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n scaling3D,\n scale3D,\n uniformScaling3D,\n uniformScale3D,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","/**\n * Some docs\n * @namespace wgpu-matrix\n */\nimport {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat3 */\n mat3: getMat3API(Mat3Ctor),\n /** @namespace mat4 */\n mat4: getMat4API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat3: mat3d,\n /**\n * 4x4 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat4: mat4d,\n /**\n * Quaternion functions that default to returning `Float64Array`\n * @namespace\n */\n quat: quatd,\n /**\n * Vec2 functions that default to returning `Float64Array`\n * @namespace\n */\n vec2: vec2d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec3: vec3d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat3: mat3n,\n /**\n * 4x4 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat4: mat4n,\n /**\n * Quaternion functions that default to returning `number[]`\n * @namespace\n */\n quat: quatn,\n /**\n * Vec2 functions that default to returning `number[]`\n * @namespace\n */\n vec2: vec2n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec3: vec3n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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h(t,o),c(o,e,o)}return{create:t,fromValues:t,set:function(t,e,r,o,c){const u=c??new n(4);return u[0]=t,u[1]=e,u[2]=r,u[3]=o,u},ceil:function(t,e){const r=e??new n(4);return r[0]=Math.ceil(t[0]),r[1]=Math.ceil(t[1]),r[2]=Math.ceil(t[2]),r[3]=Math.ceil(t[3]),r},floor:function(t,e){const r=e??new n(4);return r[0]=Math.floor(t[0]),r[1]=Math.floor(t[1]),r[2]=Math.floor(t[2]),r[3]=Math.floor(t[3]),r},round:function(t,e){const r=e??new n(4);return r[0]=Math.round(t[0]),r[1]=Math.round(t[1]),r[2]=Math.round(t[2]),r[3]=Math.round(t[3]),r},clamp:function(t,e=0,r=1,o){const c=o??new n(4);return c[0]=Math.min(r,Math.max(e,t[0])),c[1]=Math.min(r,Math.max(e,t[1])),c[2]=Math.min(r,Math.max(e,t[2])),c[3]=Math.min(r,Math.max(e,t[3])),c},add:function(t,e,r){const o=r??new n(4);return o[0]=t[0]+e[0],o[1]=t[1]+e[1],o[2]=t[2]+e[2],o[3]=t[3]+e[3],o},addScaled:function(t,e,r,o){const c=o??new n(4);return c[0]=t[0]+e[0]*r,c[1]=t[1]+e[1]*r,c[2]=t[2]+e[2]*r,c[3]=t[3]+e[3]*r,c},subtract:e,sub:e,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0])e?m(t,e,o):M(t,o)},midpoint:function(t,e,o){return r(t,e,.5,o??new n(4))}}}(n),d.set(n,t)),t}function p(n,t,e,r,o,c){return{mat3:h(n),mat4:l(t),quat:m(e),vec2:a(r),vec3:i(o),vec4:v(c)}}const{mat3:q,mat4:b,quat:g,vec2:x,vec3:y,vec4:S}=p(Float32Array,Float32Array,Float32Array,Float32Array,Float32Array,Float32Array),{mat3:A,mat4:z,quat:F,vec2:T,vec3:k,vec4:Z}=p(Float64Array,Float64Array,Float64Array,Float64Array,Float64Array,Float64Array),{mat3:I,mat4:P,quat:V,vec2:D,vec3:X,vec4:Y}=p(t,Array,Array,Array,Array,Array);n.mat3=q,n.mat3d=A,n.mat3n=I,n.mat4=b,n.mat4d=z,n.mat4n=P,n.quat=g,n.quatd=F,n.quatn=V,n.utils=c,n.vec2=x,n.vec2d=T,n.vec2n=D,n.vec3=y,n.vec3d=k,n.vec3n=X,n.vec4=S,n.vec4d=Z,n.vec4n=Y})); //# sourceMappingURL=wgpu-matrix.min.js.map diff --git a/dist/3.x/wgpu-matrix.min.js.map b/dist/3.x/wgpu-matrix.min.js.map index be7da57..047e293 100644 --- a/dist/3.x/wgpu-matrix.min.js.map +++ b/dist/3.x/wgpu-matrix.min.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nconst rotationZ = rotation;\n\n/**\n * Rotates the given 3-by-3 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotateZ = rotate;\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has two\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * two entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 3 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling3D(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2];\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 3 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale3D(m: Mat3Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in the X and Y dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling3D(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale3D(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n scaling3D,\n scale3D,\n uniformScaling3D,\n uniformScale3D,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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\ No newline at end of file diff --git a/dist/3.x/wgpu-matrix.module.js b/dist/3.x/wgpu-matrix.module.js index cdecacb..36e4e92 100644 --- a/dist/3.x/wgpu-matrix.module.js +++ b/dist/3.x/wgpu-matrix.module.js @@ -1,4 +1,4 @@ -/* wgpu-matrix@3.1.0, license MIT */ +/* wgpu-matrix@3.2.0, license MIT */ function wrapConstructor(OriginalConstructor, modifier) { return class extends OriginalConstructor { constructor(...args) { @@ -2313,9 +2313,129 @@ function getAPIImpl$3(Ctor) { } return newDst; } + /** + * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + function rotationX(angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = 1; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = c; + newDst[6] = s; + newDst[8] = 0; + newDst[9] = -s; + newDst[10] = c; + return newDst; + } + /** + * Rotates the given 3-by-3 matrix around the x-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + function rotateX(m, angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const m10 = m[4]; + const m11 = m[5]; + const m12 = m[6]; + const m20 = m[8]; + const m21 = m[9]; + const m22 = m[10]; + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[4] = c * m10 + s * m20; + newDst[5] = c * m11 + s * m21; + newDst[6] = c * m12 + s * m22; + newDst[8] = c * m20 - s * m10; + newDst[9] = c * m21 - s * m11; + newDst[10] = c * m22 - s * m12; + if (m !== newDst) { + newDst[0] = m[0]; + newDst[1] = m[1]; + newDst[2] = m[2]; + } + return newDst; + } + /** + * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + function rotationY(angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = c; + newDst[1] = 0; + newDst[2] = -s; + newDst[4] = 0; + newDst[5] = 1; + newDst[6] = 0; + newDst[8] = s; + newDst[9] = 0; + newDst[10] = c; + return newDst; + } + /** + * Rotates the given 3-by-3 matrix around the y-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + function rotateY(m, angleInRadians, dst) { + const newDst = (dst ?? new Ctor(12)); + const m00 = m[0 * 4 + 0]; + const m01 = m[0 * 4 + 1]; + const m02 = m[0 * 4 + 2]; + const m20 = m[2 * 4 + 0]; + const m21 = m[2 * 4 + 1]; + const m22 = m[2 * 4 + 2]; + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + newDst[0] = c * m00 - s * m20; + newDst[1] = c * m01 - s * m21; + newDst[2] = c * m02 - s * m22; + newDst[8] = c * m20 + s * m00; + newDst[9] = c * m21 + s * m01; + newDst[10] = c * m22 + s * m02; + if (m !== newDst) { + newDst[4] = m[4]; + newDst[5] = m[5]; + newDst[6] = m[6]; + } + return newDst; + } + /** + * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ + const rotationZ = rotation; + /** + * Rotates the given 3-by-3 matrix around the z-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ + const rotateZ = rotate; /** * Creates a 3-by-3 matrix which scales in each dimension by an amount given by - * the corresponding entry in the given vector; assumes the vector has three + * the corresponding entry in the given vector; assumes the vector has two * entries. * @param v - A vector of * 2 entries specifying the factor by which to scale in each dimension. @@ -2338,7 +2458,7 @@ function getAPIImpl$3(Ctor) { /** * Scales the given 3-by-3 matrix in each dimension by an amount * given by the corresponding entry in the given vector; assumes the vector has - * three entries. + * two entries. * @param m - The matrix to be modified. * @param v - A vector of 2 entries specifying the * factor by which to scale in each dimension. @@ -2363,7 +2483,55 @@ function getAPIImpl$3(Ctor) { return newDst; } /** - * Creates a 3-by-3 matrix which scales uniformly in each dimension + * Creates a 3-by-3 matrix which scales in each dimension by an amount given by + * the corresponding entry in the given vector; assumes the vector has three + * entries. + * @param v - A vector of + * 3 entries specifying the factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ + function scaling3D(v, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = v[0]; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = v[1]; + newDst[6] = 0; + newDst[8] = 0; + newDst[9] = 0; + newDst[10] = v[2]; + return newDst; + } + /** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given by the corresponding entry in the given vector; assumes the vector has + * three entries. + * @param m - The matrix to be modified. + * @param v - A vector of 3 entries specifying the + * factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ + function scale3D(m, v, dst) { + const newDst = (dst ?? new Ctor(12)); + const v0 = v[0]; + const v1 = v[1]; + const v2 = v[2]; + newDst[0] = v0 * m[0 * 4 + 0]; + newDst[1] = v0 * m[0 * 4 + 1]; + newDst[2] = v0 * m[0 * 4 + 2]; + newDst[4] = v1 * m[1 * 4 + 0]; + newDst[5] = v1 * m[1 * 4 + 1]; + newDst[6] = v1 * m[1 * 4 + 2]; + newDst[8] = v2 * m[2 * 4 + 0]; + newDst[9] = v2 * m[2 * 4 + 1]; + newDst[10] = v2 * m[2 * 4 + 2]; + return newDst; + } + /** + * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions * @param s - Amount to scale * @param dst - matrix to hold result. If not passed a new one is created. * @returns The scaling matrix. @@ -2382,7 +2550,7 @@ function getAPIImpl$3(Ctor) { return newDst; } /** - * Scales the given 3-by-3 matrix in each dimension by an amount + * Scales the given 3-by-3 matrix in the X and Y dimension by an amount * given. * @param m - The matrix to be modified. * @param s - Amount to scale. @@ -2404,6 +2572,46 @@ function getAPIImpl$3(Ctor) { } return newDst; } + /** + * Creates a 3-by-3 matrix which scales uniformly in each dimension + * @param s - Amount to scale + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ + function uniformScaling3D(s, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = s; + newDst[1] = 0; + newDst[2] = 0; + newDst[4] = 0; + newDst[5] = s; + newDst[6] = 0; + newDst[8] = 0; + newDst[9] = 0; + newDst[10] = s; + return newDst; + } + /** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given. + * @param m - The matrix to be modified. + * @param s - Amount to scale. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ + function uniformScale3D(m, s, dst) { + const newDst = (dst ?? new Ctor(12)); + newDst[0] = s * m[0 * 4 + 0]; + newDst[1] = s * m[0 * 4 + 1]; + newDst[2] = s * m[0 * 4 + 2]; + newDst[4] = s * m[1 * 4 + 0]; + newDst[5] = s * m[1 * 4 + 1]; + newDst[6] = s * m[1 * 4 + 2]; + newDst[8] = s * m[2 * 4 + 0]; + newDst[9] = s * m[2 * 4 + 1]; + newDst[10] = s * m[2 * 4 + 2]; + return newDst; + } return { clone, create, @@ -2431,10 +2639,20 @@ function getAPIImpl$3(Ctor) { translate, rotation, rotate, + rotationX, + rotateX, + rotationY, + rotateY, + rotationZ, + rotateZ, scaling, scale, uniformScaling, uniformScale, + scaling3D, + scale3D, + uniformScaling3D, + uniformScale3D, }; } const cache$3 = new Map(); diff --git a/dist/3.x/wgpu-matrix.module.js.map b/dist/3.x/wgpu-matrix.module.js.map index 7fa2bd8..f9545e0 100644 --- a/dist/3.x/wgpu-matrix.module.js.map +++ b/dist/3.x/wgpu-matrix.module.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","/**\n * Some docs\n * @namespace wgpu-matrix\n */\nimport {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat3 */\n mat3: getMat3API(Mat3Ctor),\n /** @namespace mat4 */\n mat4: getMat4API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat3: mat3d,\n /**\n * 4x4 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat4: mat4d,\n /**\n * Quaternion functions that default to returning `Float64Array`\n * @namespace\n */\n quat: quatd,\n /**\n * Vec2 functions that default to returning `Float64Array`\n * @namespace\n */\n vec2: vec2d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec3: vec3d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat3: mat3n,\n /**\n * 4x4 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat4: mat4n,\n /**\n * Quaternion functions that default to returning `number[]`\n * @namespace\n */\n quat: quatn,\n /**\n * Vec2 functions that default to returning `number[]`\n * @namespace\n */\n vec2: vec2n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec3: vec3n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nconst rotationZ = rotation;\n\n/**\n * Rotates the given 3-by-3 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotateZ = rotate;\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has two\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * two entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 3 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling3D(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2];\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 3 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale3D(m: Mat3Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in the X and Y dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling3D(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale3D(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n scaling3D,\n scale3D,\n uniformScaling3D,\n uniformScale3D,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","/**\n * Some docs\n * @namespace wgpu-matrix\n */\nimport {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat3 */\n mat3: getMat3API(Mat3Ctor),\n /** @namespace mat4 */\n mat4: getMat4API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat3: mat3d,\n /**\n * 4x4 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat4: mat4d,\n /**\n * Quaternion functions that default to returning `Float64Array`\n * @namespace\n */\n quat: quatd,\n /**\n * Vec2 functions that default to returning `Float64Array`\n * @namespace\n */\n vec2: vec2d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec3: vec3d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /**\n * 3x3 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat3: mat3n,\n /**\n * 4x4 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat4: mat4n,\n /**\n * Quaternion functions that default to returning `number[]`\n * @namespace\n */\n quat: quatn,\n /**\n * Vec2 functions that default to returning `number[]`\n * @namespace\n */\n vec2: vec2n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec3: vec3n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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c[0]=Math.min(e,Math.max(r,t[0])),c[1]=Math.min(e,Math.max(r,t[1])),c[2]=Math.min(e,Math.max(r,t[2])),c[3]=Math.min(e,Math.max(r,t[3])),c},add:function(t,r,e){const o=e??new n(4);return o[0]=t[0]+r[0],o[1]=t[1]+r[1],o[2]=t[2]+r[2],o[3]=t[3]+r[3],o},addScaled:function(t,r,e,o){const c=o??new n(4);return c[0]=t[0]+r[0]*e,c[1]=t[1]+r[1]*e,c[2]=t[2]+r[2]*e,c[3]=t[3]+r[3]*e,c},subtract:r,sub:r,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0])r?m(t,r,o):h(t,o)},midpoint:function(t,r,e){return o(t,r,.5,e??new n(4))}}}(n),m.set(n,t)),t}function v(n,t,r,e,o,c){return{mat3:f(n),mat4:h(t),quat:w(r),vec2:u(e),vec3:s(o),vec4:d(c)}}const{mat3:q,mat4:p,quat:b,vec2:g,vec3:x,vec4:y}=v(Float32Array,Float32Array,Float32Array,Float32Array,Float32Array,Float32Array),{mat3:A,mat4:S,quat:z,vec2:F,vec3:k,vec4:T}=v(Float64Array,Float64Array,Float64Array,Float64Array,Float64Array,Float64Array),{mat3:I,mat4:P,quat:V,vec2:Z,vec3:L,vec4:R}=v(n,Array,Array,Array,Array,Array);export{q as mat3,A as mat3d,I 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n(4);return c[0]=t[0]+e*(r[0]-t[0]),c[1]=t[1]+e*(r[1]-t[1]),c[2]=t[2]+e*(r[2]-t[2]),c[3]=t[3]+e*(r[3]-t[3]),c},length:v,len:q,lengthSq:p,lenSq:b,normalize:g,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0]).999999?(u[0]=0,u[1]=0,u[2]=0,u[3]=1,u):(t.cross(r,e,x),u[0]=x[0],u[1]=x[1],u[2]=x[2],u[3]=1+a,g(u,u))},sqlerp:function(t,r,e,o,c,u){const a=u??new n(4);return i(t,o,c,A),i(r,e,c,z),i(A,z,2*c*(1-c),a),a}}}(n),l.set(n,t)),t}const m=new Map;function d(n){let t=m.get(n);return t||(t=function(n){function t(t,r,e,o){const c=new n(4);return void 0!==t&&(c[0]=t,void 0!==r&&(c[1]=r,void 0!==e&&(c[2]=e,void 0!==o&&(c[3]=o)))),c}function r(t,r,e){const o=e??new n(4);return o[0]=t[0]-r[0],o[1]=t[1]-r[1],o[2]=t[2]-r[2],o[3]=t[3]-r[3],o}function o(t,r,e,o){const c=o??new n(4);return c[0]=t[0]+e*(r[0]-t[0]),c[1]=t[1]+e*(r[1]-t[1]),c[2]=t[2]+e*(r[2]-t[2]),c[3]=t[3]+e*(r[3]-t[3]),c}function c(t,r,e){const o=e??new n(4);return o[0]=t[0]*r,o[1]=t[1]*r,o[2]=t[2]*r,o[3]=t[3]*r,o}function u(t,r){const e=r??new n(4);return e[0]=1/t[0],e[1]=1/t[1],e[2]=1/t[2],e[3]=1/t[3],e}function a(n){const t=n[0],r=n[1],e=n[2],o=n[3];return Math.sqrt(t*t+r*r+e*e+o*o)}function s(n){const t=n[0],r=n[1],e=n[2],o=n[3];return t*t+r*r+e*e+o*o}function i(n,t){const r=n[0]-t[0],e=n[1]-t[1],o=n[2]-t[2],c=n[3]-t[3];return Math.sqrt(r*r+e*e+o*o+c*c)}function f(n,t){const r=n[0]-t[0],e=n[1]-t[1],o=n[2]-t[2],c=n[3]-t[3];return r*r+e*e+o*o+c*c}function M(t,r){const e=r??new n(4),o=t[0],c=t[1],u=t[2],a=t[3],s=Math.sqrt(o*o+c*c+u*u+a*a);return s>1e-5?(e[0]=o/s,e[1]=c/s,e[2]=u/s,e[3]=a/s):(e[0]=0,e[1]=0,e[2]=0,e[3]=0),e}function h(t,r){const e=r??new n(4);return e[0]=t[0],e[1]=t[1],e[2]=t[2],e[3]=t[3],e}function l(t,r,e){const o=e??new n(4);return o[0]=t[0]*r[0],o[1]=t[1]*r[1],o[2]=t[2]*r[2],o[3]=t[3]*r[3],o}function w(t,r,e){const o=e??new n(4);return o[0]=t[0]/r[0],o[1]=t[1]/r[1],o[2]=t[2]/r[2],o[3]=t[3]/r[3],o}function m(t,r,e){const o=e??new n(4);return M(t,o),c(o,r,o)}return{create:t,fromValues:t,set:function(t,r,e,o,c){const u=c??new n(4);return u[0]=t,u[1]=r,u[2]=e,u[3]=o,u},ceil:function(t,r){const e=r??new n(4);return e[0]=Math.ceil(t[0]),e[1]=Math.ceil(t[1]),e[2]=Math.ceil(t[2]),e[3]=Math.ceil(t[3]),e},floor:function(t,r){const e=r??new n(4);return e[0]=Math.floor(t[0]),e[1]=Math.floor(t[1]),e[2]=Math.floor(t[2]),e[3]=Math.floor(t[3]),e},round:function(t,r){const e=r??new n(4);return e[0]=Math.round(t[0]),e[1]=Math.round(t[1]),e[2]=Math.round(t[2]),e[3]=Math.round(t[3]),e},clamp:function(t,r=0,e=1,o){const c=o??new n(4);return c[0]=Math.min(e,Math.max(r,t[0])),c[1]=Math.min(e,Math.max(r,t[1])),c[2]=Math.min(e,Math.max(r,t[2])),c[3]=Math.min(e,Math.max(r,t[3])),c},add:function(t,r,e){const o=e??new n(4);return o[0]=t[0]+r[0],o[1]=t[1]+r[1],o[2]=t[2]+r[2],o[3]=t[3]+r[3],o},addScaled:function(t,r,e,o){const c=o??new n(4);return c[0]=t[0]+r[0]*e,c[1]=t[1]+r[1]*e,c[2]=t[2]+r[2]*e,c[3]=t[3]+r[3]*e,c},subtract:r,sub:r,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0])r?m(t,r,o):h(t,o)},midpoint:function(t,r,e){return o(t,r,.5,e??new n(4))}}}(n),m.set(n,t)),t}function v(n,t,r,e,o,c){return{mat3:f(n),mat4:h(t),quat:w(r),vec2:u(e),vec3:s(o),vec4:d(c)}}const{mat3:q,mat4:p,quat:b,vec2:g,vec3:x,vec4:y}=v(Float32Array,Float32Array,Float32Array,Float32Array,Float32Array,Float32Array),{mat3:S,mat4:A,quat:z,vec2:F,vec3:k,vec4:T}=v(Float64Array,Float64Array,Float64Array,Float64Array,Float64Array,Float64Array),{mat3:Z,mat4:I,quat:P,vec2:V,vec3:D,vec4:X}=v(n,Array,Array,Array,Array,Array);export{q as mat3,S as mat3d,Z as mat3n,p as mat4,A as mat4d,I as mat4n,b as quat,z as quatd,P as quatn,o as utils,g as vec2,F as vec2d,V as vec2n,x as vec3,k as vec3d,D as vec3n,y as vec4,T as vec4d,X as vec4n}; //# sourceMappingURL=wgpu-matrix.module.min.js.map diff --git a/dist/3.x/wgpu-matrix.module.min.js.map b/dist/3.x/wgpu-matrix.module.min.js.map index c2d1801..7859fbb 100644 --- a/dist/3.x/wgpu-matrix.module.min.js.map +++ b/dist/3.x/wgpu-matrix.module.min.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.module.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.module.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/vec3-impl.ts","../../../src/mat3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n const vec3 = getVec3API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n/**\n * Returns the \"2d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction get3DScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec3.create());\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nconst rotationZ = rotation;\n\n/**\n * Rotates the given 3-by-3 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotateZ = rotate;\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has two\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * two entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 3 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling3D(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2];\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 3 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale3D(m: Mat3Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in the X and Y dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling3D(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale3D(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n get3DScaling,\n translation,\n translate,\n rotation,\n rotate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n scaling3D,\n scale3D,\n uniformScaling3D,\n uniformScale3D,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n/**\n * Returns the \"3d\" scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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"; \ No newline at end of file diff --git a/docs/functions/mat3.rotateX.html b/docs/functions/mat3.rotateX.html new file mode 100644 index 0000000..acdd47d --- /dev/null +++ b/docs/functions/mat3.rotateX.html @@ -0,0 +1,7 @@ +rotateX | wgpu-matrix

Function rotateX

  • rotateX<T>(m, angleInRadians, dst?): T

  • Rotates the given 3-by-3 matrix around the x-axis by the given +angle.

    +

    Type Parameters

    Parameters

    • m: BaseArgType

      The matrix.

      +
    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotated matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.rotateY.html b/docs/functions/mat3.rotateY.html new file mode 100644 index 0000000..bd4647a --- /dev/null +++ b/docs/functions/mat3.rotateY.html @@ -0,0 +1,7 @@ +rotateY | wgpu-matrix

Function rotateY

  • rotateY<T>(m, angleInRadians, dst?): T

  • Rotates the given 3-by-3 matrix around the y-axis by the given +angle.

    +

    Type Parameters

    Parameters

    • m: BaseArgType

      The matrix.

      +
    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotated matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.rotateZ.html b/docs/functions/mat3.rotateZ.html new file mode 100644 index 0000000..243b3c1 --- /dev/null +++ b/docs/functions/mat3.rotateZ.html @@ -0,0 +1,6 @@ +rotateZ | wgpu-matrix

Function rotateZ

  • rotateZ<T>(m, angleInRadians, dst?): T

  • Rotates the given 3-by-3 matrix by the given angle.

    +

    Type Parameters

    Parameters

    • m: BaseArgType

      The matrix.

      +
    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotated matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.rotationX.html b/docs/functions/mat3.rotationX.html new file mode 100644 index 0000000..2aaff9b --- /dev/null +++ b/docs/functions/mat3.rotationX.html @@ -0,0 +1,5 @@ +rotationX | wgpu-matrix

Function rotationX

  • rotationX<T>(angleInRadians, dst?): T

  • Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.

    +

    Type Parameters

    Parameters

    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotation matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.rotationY.html b/docs/functions/mat3.rotationY.html new file mode 100644 index 0000000..a5f418a --- /dev/null +++ b/docs/functions/mat3.rotationY.html @@ -0,0 +1,5 @@ +rotationY | wgpu-matrix

Function rotationY

  • rotationY<T>(angleInRadians, dst?): T

  • Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.

    +

    Type Parameters

    Parameters

    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotation matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.rotationZ.html b/docs/functions/mat3.rotationZ.html new file mode 100644 index 0000000..28e167f --- /dev/null +++ b/docs/functions/mat3.rotationZ.html @@ -0,0 +1,5 @@ +rotationZ | wgpu-matrix

Function rotationZ

  • rotationZ<T>(angleInRadians, dst?): T

  • Creates a 3-by-3 matrix which rotates by the given angle.

    +

    Type Parameters

    Parameters

    • angleInRadians: number

      The angle by which to rotate (in radians).

      +
    • Optional dst: T

      matrix to hold result. If not passed a new one is created.

      +

    Returns T

    The rotation matrix.

    +

Settings

Member Visibility
\ No newline at end of file diff --git a/docs/functions/mat3.scale.html b/docs/functions/mat3.scale.html index 3eef542..c48016a 100644 --- a/docs/functions/mat3.scale.html +++ b/docs/functions/mat3.scale.html @@ -1,6 +1,6 @@ scale | wgpu-matrix

Function scale

  • scale<T>(m, v, dst?): T

  • Scales the given 3-by-3 matrix in each dimension by an amount given by the corresponding entry in the given vector; assumes the vector has -three entries.

    +two entries.

    Type Parameters

    Parameters

    • m: BaseArgType

      The matrix to be modified.

    • v: BaseArgType

      A vector of 2 entries specifying the factor by which to scale in each dimension.

      diff --git a/docs/functions/mat3.scale3D.html b/docs/functions/mat3.scale3D.html new file mode 100644 index 0000000..41efd52 --- /dev/null +++ b/docs/functions/mat3.scale3D.html @@ -0,0 +1,9 @@ +scale3D | wgpu-matrix

      Function scale3D

      • scale3D<T>(m, v, dst?): T

      • Scales the given 3-by-3 matrix in each dimension by an amount +given by the corresponding entry in the given vector; assumes the vector has +three entries.

        +

        Type Parameters

        Parameters

        • m: BaseArgType

          The matrix to be modified.

          +
        • v: BaseArgType

          A vector of 3 entries specifying the +factor by which to scale in each dimension.

          +
        • Optional dst: T

          matrix to hold result. If not passed a new one is created.

          +

        Returns T

        The scaled matrix.

        +

      Settings

      Member Visibility
      \ No newline at end of file diff --git a/docs/functions/mat3.scaling.html b/docs/functions/mat3.scaling.html index 236246d..c0dab28 100644 --- a/docs/functions/mat3.scaling.html +++ b/docs/functions/mat3.scaling.html @@ -1,5 +1,5 @@ scaling | wgpu-matrix

      Function scaling

      • scaling<T>(v, dst?): T

      • Creates a 3-by-3 matrix which scales in each dimension by an amount given by -the corresponding entry in the given vector; assumes the vector has three +the corresponding entry in the given vector; assumes the vector has two entries.

        Type Parameters

        Parameters

        • v: BaseArgType

          A vector of 2 entries specifying the factor by which to scale in each dimension.

          diff --git a/docs/functions/mat3.scaling3D.html b/docs/functions/mat3.scaling3D.html new file mode 100644 index 0000000..781c3e0 --- /dev/null +++ b/docs/functions/mat3.scaling3D.html @@ -0,0 +1,8 @@ +scaling3D | wgpu-matrix

          Function scaling3D

          • scaling3D<T>(v, dst?): T

          • Creates a 3-by-3 matrix which scales in each dimension by an amount given by +the corresponding entry in the given vector; assumes the vector has three +entries.

            +

            Type Parameters

            Parameters

            • v: BaseArgType

              A vector of +3 entries specifying the factor by which to scale in each dimension.

              +
            • Optional dst: T

              matrix to hold result. If not passed a new one is created.

              +

            Returns T

            The scaling matrix.

            +

          Settings

          Member Visibility
          \ No newline at end of file diff --git a/docs/functions/mat3.uniformScale.html b/docs/functions/mat3.uniformScale.html index 186410e..ec32e3a 100644 --- a/docs/functions/mat3.uniformScale.html +++ b/docs/functions/mat3.uniformScale.html @@ -1,4 +1,4 @@ -uniformScale | wgpu-matrix

          Function uniformScale

          • uniformScale<T>(m, s, dst?): T

          • Scales the given 3-by-3 matrix in each dimension by an amount +uniformScale | wgpu-matrix

            Function uniformScale

            • uniformScale<T>(m, s, dst?): T

            • Scales the given 3-by-3 matrix in the X and Y dimension by an amount given.

              Type Parameters

              Parameters

              • m: BaseArgType

                The matrix to be modified.

              • s: number

                Amount to scale.

                diff --git a/docs/functions/mat3.uniformScale3D.html b/docs/functions/mat3.uniformScale3D.html new file mode 100644 index 0000000..61deb37 --- /dev/null +++ b/docs/functions/mat3.uniformScale3D.html @@ -0,0 +1,7 @@ +uniformScale3D | wgpu-matrix

                Function uniformScale3D

                • uniformScale3D<T>(m, s, dst?): T

                • Scales the given 3-by-3 matrix in each dimension by an amount +given.

                  +

                  Type Parameters

                  Parameters

                  • m: BaseArgType

                    The matrix to be modified.

                    +
                  • s: number

                    Amount to scale.

                    +
                  • Optional dst: T

                    matrix to hold result. If not passed a new one is created.

                    +

                  Returns T

                  The scaled matrix.

                  +

                Settings

                Member Visibility
                \ No newline at end of file diff --git a/docs/functions/mat3.uniformScaling.html b/docs/functions/mat3.uniformScaling.html index c5c3535..7ae071d 100644 --- a/docs/functions/mat3.uniformScaling.html +++ b/docs/functions/mat3.uniformScaling.html @@ -1,4 +1,4 @@ -uniformScaling | wgpu-matrix

                Function uniformScaling

                • uniformScaling<T>(s, dst?): T

                • Creates a 3-by-3 matrix which scales uniformly in each dimension

                  +uniformScaling | wgpu-matrix

                  Function uniformScaling

                  • uniformScaling<T>(s, dst?): T

                  • Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions

                    Type Parameters

                    Parameters

                    • s: number

                      Amount to scale

                    • Optional dst: T

                      matrix to hold result. If not passed a new one is created.

                    Returns T

                    The scaling matrix.

                    diff --git a/docs/functions/mat3.uniformScaling3D.html b/docs/functions/mat3.uniformScaling3D.html new file mode 100644 index 0000000..7367363 --- /dev/null +++ b/docs/functions/mat3.uniformScaling3D.html @@ -0,0 +1,5 @@ +uniformScaling3D | wgpu-matrix

                    Function uniformScaling3D

                    • uniformScaling3D<T>(s, dst?): T

                    • Creates a 3-by-3 matrix which scales uniformly in each dimension

                      +

                      Type Parameters

                      Parameters

                      • s: number

                        Amount to scale

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The scaling matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotateX.html b/docs/functions/mat3d.rotateX.html new file mode 100644 index 0000000..3333dc2 --- /dev/null +++ b/docs/functions/mat3d.rotateX.html @@ -0,0 +1,7 @@ +rotateX | wgpu-matrix

                    Function rotateX

                    • rotateX<T>(m, angleInRadians, dst?): T

                    • Rotates the given 3-by-3 matrix around the x-axis by the given +angle.

                      +

                      Type Parameters

                      Parameters

                      • m: BaseArgType

                        The matrix.

                        +
                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotated matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotateY.html b/docs/functions/mat3d.rotateY.html new file mode 100644 index 0000000..b2e2af5 --- /dev/null +++ b/docs/functions/mat3d.rotateY.html @@ -0,0 +1,7 @@ +rotateY | wgpu-matrix

                    Function rotateY

                    • rotateY<T>(m, angleInRadians, dst?): T

                    • Rotates the given 3-by-3 matrix around the y-axis by the given +angle.

                      +

                      Type Parameters

                      Parameters

                      • m: BaseArgType

                        The matrix.

                        +
                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotated matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotateZ.html b/docs/functions/mat3d.rotateZ.html new file mode 100644 index 0000000..ea3f4ad --- /dev/null +++ b/docs/functions/mat3d.rotateZ.html @@ -0,0 +1,6 @@ +rotateZ | wgpu-matrix

                    Function rotateZ

                    • rotateZ<T>(m, angleInRadians, dst?): T

                    • Rotates the given 3-by-3 matrix by the given angle.

                      +

                      Type Parameters

                      Parameters

                      • m: BaseArgType

                        The matrix.

                        +
                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotated matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotationX.html b/docs/functions/mat3d.rotationX.html new file mode 100644 index 0000000..edc0c66 --- /dev/null +++ b/docs/functions/mat3d.rotationX.html @@ -0,0 +1,5 @@ +rotationX | wgpu-matrix

                    Function rotationX

                    • rotationX<T>(angleInRadians, dst?): T

                    • Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.

                      +

                      Type Parameters

                      Parameters

                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotation matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotationY.html b/docs/functions/mat3d.rotationY.html new file mode 100644 index 0000000..f8130a5 --- /dev/null +++ b/docs/functions/mat3d.rotationY.html @@ -0,0 +1,5 @@ +rotationY | wgpu-matrix

                    Function rotationY

                    • rotationY<T>(angleInRadians, dst?): T

                    • Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.

                      +

                      Type Parameters

                      Parameters

                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotation matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.rotationZ.html b/docs/functions/mat3d.rotationZ.html new file mode 100644 index 0000000..d90cccf --- /dev/null +++ b/docs/functions/mat3d.rotationZ.html @@ -0,0 +1,5 @@ +rotationZ | wgpu-matrix

                    Function rotationZ

                    • rotationZ<T>(angleInRadians, dst?): T

                    • Creates a 3-by-3 matrix which rotates by the given angle.

                      +

                      Type Parameters

                      Parameters

                      • angleInRadians: number

                        The angle by which to rotate (in radians).

                        +
                      • Optional dst: T

                        matrix to hold result. If not passed a new one is created.

                        +

                      Returns T

                      The rotation matrix.

                      +

                    Settings

                    Member Visibility
                    \ No newline at end of file diff --git a/docs/functions/mat3d.scale.html b/docs/functions/mat3d.scale.html index 939e38f..4d1bd00 100644 --- a/docs/functions/mat3d.scale.html +++ b/docs/functions/mat3d.scale.html @@ -1,6 +1,6 @@ scale | wgpu-matrix

                    Function scale

                    • scale<T>(m, v, dst?): T

                    • Scales the given 3-by-3 matrix in each dimension by an amount given by the corresponding entry in the given vector; assumes the vector has -three entries.

                      +two entries.

                      Type Parameters

                      Parameters

                      • m: BaseArgType

                        The matrix to be modified.

                      • v: BaseArgType

                        A vector of 2 entries specifying the factor by which to scale in each dimension.

                        diff --git a/docs/functions/mat3d.scale3D.html b/docs/functions/mat3d.scale3D.html new file mode 100644 index 0000000..365f84a --- /dev/null +++ b/docs/functions/mat3d.scale3D.html @@ -0,0 +1,9 @@ +scale3D | wgpu-matrix

                        Function scale3D

                        • scale3D<T>(m, v, dst?): T

                        • Scales the given 3-by-3 matrix in each dimension by an amount +given by the corresponding entry in the given vector; assumes the vector has +three entries.

                          +

                          Type Parameters

                          Parameters

                          • m: BaseArgType

                            The matrix to be modified.

                            +
                          • v: BaseArgType

                            A vector of 3 entries specifying the +factor by which to scale in each dimension.

                            +
                          • Optional dst: T

                            matrix to hold result. If not passed a new one is created.

                            +

                          Returns T

                          The scaled matrix.

                          +

                        Settings

                        Member Visibility
                        \ No newline at end of file diff --git a/docs/functions/mat3d.scaling.html b/docs/functions/mat3d.scaling.html index fa0039a..284edd5 100644 --- a/docs/functions/mat3d.scaling.html +++ b/docs/functions/mat3d.scaling.html @@ -1,5 +1,5 @@ scaling | wgpu-matrix

                        Function scaling

                        • scaling<T>(v, dst?): T

                        • Creates a 3-by-3 matrix which scales in each dimension by an amount given by -the corresponding entry in the given vector; assumes the vector has three +the corresponding entry in the given vector; assumes the vector has two entries.

                          Type Parameters

                          Parameters

                          • v: BaseArgType

                            A vector of 2 entries specifying the factor by which to scale in each dimension.

                            diff --git a/docs/functions/mat3d.scaling3D.html b/docs/functions/mat3d.scaling3D.html new file mode 100644 index 0000000..a53d9f5 --- /dev/null +++ b/docs/functions/mat3d.scaling3D.html @@ -0,0 +1,8 @@ +scaling3D | wgpu-matrix

                            Function scaling3D

                            • scaling3D<T>(v, dst?): T

                            • Creates a 3-by-3 matrix which scales in each dimension by an amount given by +the corresponding entry in the given vector; assumes the vector has three +entries.

                              +

                              Type Parameters

                              Parameters

                              • v: BaseArgType

                                A vector of +3 entries specifying the factor by which to scale in each dimension.

                                +
                              • Optional dst: T

                                matrix to hold result. If not passed a new one is created.

                                +

                              Returns T

                              The scaling matrix.

                              +

                            Settings

                            Member Visibility
                            \ No newline at end of file diff --git a/docs/functions/mat3d.uniformScale.html b/docs/functions/mat3d.uniformScale.html index 9ca932b..3dfc43d 100644 --- a/docs/functions/mat3d.uniformScale.html +++ b/docs/functions/mat3d.uniformScale.html @@ -1,4 +1,4 @@ -uniformScale | wgpu-matrix

                            Function uniformScale

                            • uniformScale<T>(m, s, dst?): T

                            • Scales the given 3-by-3 matrix in each dimension by an amount +uniformScale | wgpu-matrix

                              Function uniformScale

                              • uniformScale<T>(m, s, dst?): T

                              • Scales the given 3-by-3 matrix in the X and Y dimension by an amount given.

                                Type Parameters

                                Parameters

                                • m: BaseArgType

                                  The matrix to be modified.

                                • s: number

                                  Amount to scale.

                                  diff --git a/docs/functions/mat3d.uniformScale3D.html b/docs/functions/mat3d.uniformScale3D.html new file mode 100644 index 0000000..78c2c16 --- /dev/null +++ b/docs/functions/mat3d.uniformScale3D.html @@ -0,0 +1,7 @@ +uniformScale3D | wgpu-matrix

                                  Function uniformScale3D

                                  • uniformScale3D<T>(m, s, dst?): T

                                  • Scales the given 3-by-3 matrix in each dimension by an amount +given.

                                    +

                                    Type Parameters

                                    Parameters

                                    • m: BaseArgType

                                      The matrix to be modified.

                                      +
                                    • s: number

                                      Amount to scale.

                                      +
                                    • Optional dst: T

                                      matrix to hold result. If not passed a new one is created.

                                      +

                                    Returns T

                                    The scaled matrix.

                                    +

                                  Settings

                                  Member Visibility
                                  \ No newline at end of file diff --git a/docs/functions/mat3d.uniformScaling.html b/docs/functions/mat3d.uniformScaling.html index d6971ff..2363f92 100644 --- a/docs/functions/mat3d.uniformScaling.html +++ b/docs/functions/mat3d.uniformScaling.html @@ -1,4 +1,4 @@ -uniformScaling | wgpu-matrix

                                  Function uniformScaling

                                  • uniformScaling<T>(s, dst?): T

                                  • Creates a 3-by-3 matrix which scales uniformly in each dimension

                                    +uniformScaling | wgpu-matrix

                                    Function uniformScaling

                                    • uniformScaling<T>(s, dst?): T

                                    • Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions

                                      Type Parameters

                                      Parameters

                                      • s: number

                                        Amount to scale

                                      • Optional dst: T

                                        matrix to hold result. If not passed a new one is created.

                                      Returns T

                                      The scaling matrix.

                                      diff --git a/docs/functions/mat3d.uniformScaling3D.html b/docs/functions/mat3d.uniformScaling3D.html new file mode 100644 index 0000000..6a35770 --- /dev/null +++ b/docs/functions/mat3d.uniformScaling3D.html @@ -0,0 +1,5 @@ +uniformScaling3D | wgpu-matrix

                                      Function uniformScaling3D

                                      • uniformScaling3D<T>(s, dst?): T

                                      • Creates a 3-by-3 matrix which scales uniformly in each dimension

                                        +

                                        Type Parameters

                                        Parameters

                                        • s: number

                                          Amount to scale

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The scaling matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotateX.html b/docs/functions/mat3n.rotateX.html new file mode 100644 index 0000000..ea1bc9f --- /dev/null +++ b/docs/functions/mat3n.rotateX.html @@ -0,0 +1,7 @@ +rotateX | wgpu-matrix

                                      Function rotateX

                                      • rotateX<T>(m, angleInRadians, dst?): T

                                      • Rotates the given 3-by-3 matrix around the x-axis by the given +angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • m: BaseArgType

                                          The matrix.

                                          +
                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotated matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotateY.html b/docs/functions/mat3n.rotateY.html new file mode 100644 index 0000000..a6e6d54 --- /dev/null +++ b/docs/functions/mat3n.rotateY.html @@ -0,0 +1,7 @@ +rotateY | wgpu-matrix

                                      Function rotateY

                                      • rotateY<T>(m, angleInRadians, dst?): T

                                      • Rotates the given 3-by-3 matrix around the y-axis by the given +angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • m: BaseArgType

                                          The matrix.

                                          +
                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotated matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotateZ.html b/docs/functions/mat3n.rotateZ.html new file mode 100644 index 0000000..738cf93 --- /dev/null +++ b/docs/functions/mat3n.rotateZ.html @@ -0,0 +1,6 @@ +rotateZ | wgpu-matrix

                                      Function rotateZ

                                      • rotateZ<T>(m, angleInRadians, dst?): T

                                      • Rotates the given 3-by-3 matrix by the given angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • m: BaseArgType

                                          The matrix.

                                          +
                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotated matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotationX.html b/docs/functions/mat3n.rotationX.html new file mode 100644 index 0000000..1ccad6d --- /dev/null +++ b/docs/functions/mat3n.rotationX.html @@ -0,0 +1,5 @@ +rotationX | wgpu-matrix

                                      Function rotationX

                                      • rotationX<T>(angleInRadians, dst?): T

                                      • Creates a 3-by-3 matrix which rotates around the x-axis by the given angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotation matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotationY.html b/docs/functions/mat3n.rotationY.html new file mode 100644 index 0000000..83315da --- /dev/null +++ b/docs/functions/mat3n.rotationY.html @@ -0,0 +1,5 @@ +rotationY | wgpu-matrix

                                      Function rotationY

                                      • rotationY<T>(angleInRadians, dst?): T

                                      • Creates a 3-by-3 matrix which rotates around the y-axis by the given angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotation matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.rotationZ.html b/docs/functions/mat3n.rotationZ.html new file mode 100644 index 0000000..81c6423 --- /dev/null +++ b/docs/functions/mat3n.rotationZ.html @@ -0,0 +1,5 @@ +rotationZ | wgpu-matrix

                                      Function rotationZ

                                      • rotationZ<T>(angleInRadians, dst?): T

                                      • Creates a 3-by-3 matrix which rotates by the given angle.

                                        +

                                        Type Parameters

                                        Parameters

                                        • angleInRadians: number

                                          The angle by which to rotate (in radians).

                                          +
                                        • Optional dst: T

                                          matrix to hold result. If not passed a new one is created.

                                          +

                                        Returns T

                                        The rotation matrix.

                                        +

                                      Settings

                                      Member Visibility
                                      \ No newline at end of file diff --git a/docs/functions/mat3n.scale.html b/docs/functions/mat3n.scale.html index 3e40c5b..6bfcc60 100644 --- a/docs/functions/mat3n.scale.html +++ b/docs/functions/mat3n.scale.html @@ -1,6 +1,6 @@ scale | wgpu-matrix

                                      Function scale

                                      • scale<T>(m, v, dst?): T

                                      • Scales the given 3-by-3 matrix in each dimension by an amount given by the corresponding entry in the given vector; assumes the vector has -three entries.

                                        +two entries.

                                        Type Parameters

                                        Parameters

                                        • m: BaseArgType

                                          The matrix to be modified.

                                        • v: BaseArgType

                                          A vector of 2 entries specifying the factor by which to scale in each dimension.

                                          diff --git a/docs/functions/mat3n.scale3D.html b/docs/functions/mat3n.scale3D.html new file mode 100644 index 0000000..0ea4c0a --- /dev/null +++ b/docs/functions/mat3n.scale3D.html @@ -0,0 +1,9 @@ +scale3D | wgpu-matrix

                                          Function scale3D

                                          • scale3D<T>(m, v, dst?): T

                                          • Scales the given 3-by-3 matrix in each dimension by an amount +given by the corresponding entry in the given vector; assumes the vector has +three entries.

                                            +

                                            Type Parameters

                                            Parameters

                                            • m: BaseArgType

                                              The matrix to be modified.

                                              +
                                            • v: BaseArgType

                                              A vector of 3 entries specifying the +factor by which to scale in each dimension.

                                              +
                                            • Optional dst: T

                                              matrix to hold result. If not passed a new one is created.

                                              +

                                            Returns T

                                            The scaled matrix.

                                            +

                                          Settings

                                          Member Visibility
                                          \ No newline at end of file diff --git a/docs/functions/mat3n.scaling.html b/docs/functions/mat3n.scaling.html index 40bc75b..123ca7a 100644 --- a/docs/functions/mat3n.scaling.html +++ b/docs/functions/mat3n.scaling.html @@ -1,5 +1,5 @@ scaling | wgpu-matrix

                                          Function scaling

                                          • scaling<T>(v, dst?): T

                                          • Creates a 3-by-3 matrix which scales in each dimension by an amount given by -the corresponding entry in the given vector; assumes the vector has three +the corresponding entry in the given vector; assumes the vector has two entries.

                                            Type Parameters

                                            Parameters

                                            • v: BaseArgType

                                              A vector of 2 entries specifying the factor by which to scale in each dimension.

                                              diff --git a/docs/functions/mat3n.scaling3D.html b/docs/functions/mat3n.scaling3D.html new file mode 100644 index 0000000..4ca77bf --- /dev/null +++ b/docs/functions/mat3n.scaling3D.html @@ -0,0 +1,8 @@ +scaling3D | wgpu-matrix

                                              Function scaling3D

                                              • scaling3D<T>(v, dst?): T

                                              • Creates a 3-by-3 matrix which scales in each dimension by an amount given by +the corresponding entry in the given vector; assumes the vector has three +entries.

                                                +

                                                Type Parameters

                                                Parameters

                                                • v: BaseArgType

                                                  A vector of +3 entries specifying the factor by which to scale in each dimension.

                                                  +
                                                • Optional dst: T

                                                  matrix to hold result. If not passed a new one is created.

                                                  +

                                                Returns T

                                                The scaling matrix.

                                                +

                                              Settings

                                              Member Visibility
                                              \ No newline at end of file diff --git a/docs/functions/mat3n.uniformScale.html b/docs/functions/mat3n.uniformScale.html index aa0194e..788845a 100644 --- a/docs/functions/mat3n.uniformScale.html +++ b/docs/functions/mat3n.uniformScale.html @@ -1,4 +1,4 @@ -uniformScale | wgpu-matrix

                                              Function uniformScale

                                              • uniformScale<T>(m, s, dst?): T

                                              • Scales the given 3-by-3 matrix in each dimension by an amount +uniformScale | wgpu-matrix

                                                Function uniformScale

                                                • uniformScale<T>(m, s, dst?): T

                                                • Scales the given 3-by-3 matrix in the X and Y dimension by an amount given.

                                                  Type Parameters

                                                  Parameters

                                                  • m: BaseArgType

                                                    The matrix to be modified.

                                                  • s: number

                                                    Amount to scale.

                                                    diff --git a/docs/functions/mat3n.uniformScale3D.html b/docs/functions/mat3n.uniformScale3D.html new file mode 100644 index 0000000..0809025 --- /dev/null +++ b/docs/functions/mat3n.uniformScale3D.html @@ -0,0 +1,7 @@ +uniformScale3D | wgpu-matrix

                                                    Function uniformScale3D

                                                    • uniformScale3D<T>(m, s, dst?): T

                                                    • Scales the given 3-by-3 matrix in each dimension by an amount +given.

                                                      +

                                                      Type Parameters

                                                      Parameters

                                                      • m: BaseArgType

                                                        The matrix to be modified.

                                                        +
                                                      • s: number

                                                        Amount to scale.

                                                        +
                                                      • Optional dst: T

                                                        matrix to hold result. If not passed a new one is created.

                                                        +

                                                      Returns T

                                                      The scaled matrix.

                                                      +

                                                    Settings

                                                    Member Visibility
                                                    \ No newline at end of file diff --git a/docs/functions/mat3n.uniformScaling.html b/docs/functions/mat3n.uniformScaling.html index 3aab7bf..3131fde 100644 --- a/docs/functions/mat3n.uniformScaling.html +++ b/docs/functions/mat3n.uniformScaling.html @@ -1,4 +1,4 @@ -uniformScaling | wgpu-matrix

                                                    Function uniformScaling

                                                    • uniformScaling<T>(s, dst?): T

                                                    • Creates a 3-by-3 matrix which scales uniformly in each dimension

                                                      +uniformScaling | wgpu-matrix

                                                      Function uniformScaling

                                                      • uniformScaling<T>(s, dst?): T

                                                      • Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions

                                                        Type Parameters

                                                        Parameters

                                                        • s: number

                                                          Amount to scale

                                                        • Optional dst: T

                                                          matrix to hold result. If not passed a new one is created.

                                                        Returns T

                                                        The scaling matrix.

                                                        diff --git a/docs/functions/mat3n.uniformScaling3D.html b/docs/functions/mat3n.uniformScaling3D.html new file mode 100644 index 0000000..95ee942 --- /dev/null +++ b/docs/functions/mat3n.uniformScaling3D.html @@ -0,0 +1,5 @@ +uniformScaling3D | wgpu-matrix

                                                        Function uniformScaling3D

                                                        • uniformScaling3D<T>(s, dst?): T

                                                        • Creates a 3-by-3 matrix which scales uniformly in each dimension

                                                          +

                                                          Type Parameters

                                                          Parameters

                                                          • s: number

                                                            Amount to scale

                                                            +
                                                          • Optional dst: T

                                                            matrix to hold result. If not passed a new one is created.

                                                            +

                                                          Returns T

                                                          The scaling matrix.

                                                          +

                                                        Settings

                                                        Member Visibility
                                                        \ No newline at end of file diff --git a/docs/modules/mat3.html b/docs/modules/mat3.html index 473f8e9..1a37e85 100644 --- a/docs/modules/mat3.html +++ b/docs/modules/mat3.html @@ -18,9 +18,17 @@ multiply negate rotate +rotateX +rotateY +rotateZ rotation +rotationX +rotationY +rotationZ scale +scale3D scaling +scaling3D set setAxis setTranslation @@ -28,5 +36,7 @@ translation transpose uniformScale +uniformScale3D uniformScaling +uniformScaling3D

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                                              \ No newline at end of file diff --git a/docs/modules/mat3d.html b/docs/modules/mat3d.html index 7460727..c074857 100644 --- a/docs/modules/mat3d.html +++ b/docs/modules/mat3d.html @@ -18,9 +18,17 @@ multiply negate rotate +rotateX +rotateY +rotateZ rotation +rotationX +rotationY +rotationZ scale +scale3D scaling +scaling3D set setAxis setTranslation @@ -28,5 +36,7 @@ translation transpose uniformScale +uniformScale3D uniformScaling +uniformScaling3D

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                                    \ No newline at end of file diff --git a/docs/modules/mat3n.html b/docs/modules/mat3n.html index cf9360c..60d1ad8 100644 --- a/docs/modules/mat3n.html +++ b/docs/modules/mat3n.html @@ -18,9 +18,17 @@ multiply negate rotate +rotateX +rotateY +rotateZ rotation +rotationX +rotationY +rotationZ scale +scale3D scaling +scaling3D set setAxis setTranslation @@ -28,5 +36,7 @@ translation transpose uniformScale +uniformScale3D uniformScaling +uniformScaling3D

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                            \ No newline at end of file diff --git a/package-lock.json b/package-lock.json index d3fb832..535bb09 100644 --- a/package-lock.json +++ b/package-lock.json @@ -1,12 +1,12 @@ { "name": "wgpu-matrix", - "version": "3.1.0", + "version": "3.2.0", "lockfileVersion": 3, "requires": true, "packages": { "": { "name": "wgpu-matrix", - "version": "3.1.0", + "version": "3.2.0", "license": "MIT", "devDependencies": { "@rollup/plugin-terser": "^0.4.4", diff --git a/package.json b/package.json index d688327..5f26743 100644 --- a/package.json +++ b/package.json @@ -1,6 +1,6 @@ { "name": "wgpu-matrix", - "version": "3.1.0", + "version": "3.2.0", "description": "fast matrix math library for WebGPU", "main": "dist/3.x/wgpu-matrix.module.js", "module": "dist/3.x/wgpu-matrix.module.js", diff --git a/src/mat3-impl.ts b/src/mat3-impl.ts index 40c935e..abf0e07 100644 --- a/src/mat3-impl.ts +++ b/src/mat3-impl.ts @@ -661,9 +661,138 @@ function rotate(m: Mat3Arg, angleInRadians: number, return newDst; } +/** + * Creates a 3-by-3 matrix which rotates around the x-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ +function rotationX(angleInRadians: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + + newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; + newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; + newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; + + return newDst; +} + +/** + * Rotates the given 3-by-3 matrix around the x-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ +function rotateX(m: Mat3Arg, angleInRadians: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + const m10 = m[4]; + const m11 = m[5]; + const m12 = m[6]; + const m20 = m[8]; + const m21 = m[9]; + const m22 = m[10]; + + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + + newDst[4] = c * m10 + s * m20; + newDst[5] = c * m11 + s * m21; + newDst[6] = c * m12 + s * m22; + newDst[8] = c * m20 - s * m10; + newDst[9] = c * m21 - s * m11; + newDst[10] = c * m22 - s * m12; + + if (m !== newDst) { + newDst[ 0] = m[ 0]; + newDst[ 1] = m[ 1]; + newDst[ 2] = m[ 2]; + } + + return newDst; +} + +/** + * Creates a 3-by-3 matrix which rotates around the y-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ +function rotationY(angleInRadians: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + + newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; + newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; + newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; + + return newDst; +} + +/** + * Rotates the given 3-by-3 matrix around the y-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ +function rotateY(m: Mat3Arg, angleInRadians: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + const m00 = m[0 * 4 + 0]; + const m01 = m[0 * 4 + 1]; + const m02 = m[0 * 4 + 2]; + const m20 = m[2 * 4 + 0]; + const m21 = m[2 * 4 + 1]; + const m22 = m[2 * 4 + 2]; + const c = Math.cos(angleInRadians); + const s = Math.sin(angleInRadians); + + newDst[ 0] = c * m00 - s * m20; + newDst[ 1] = c * m01 - s * m21; + newDst[ 2] = c * m02 - s * m22; + newDst[ 8] = c * m20 + s * m00; + newDst[ 9] = c * m21 + s * m01; + newDst[10] = c * m22 + s * m02; + + if (m !== newDst) { + newDst[ 4] = m[ 4]; + newDst[ 5] = m[ 5]; + newDst[ 6] = m[ 6]; + } + + return newDst; +} + +/** + * Creates a 3-by-3 matrix which rotates around the z-axis by the given angle. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotation matrix. + */ +const rotationZ = rotation; + +/** + * Rotates the given 3-by-3 matrix around the z-axis by the given + * angle. + * @param m - The matrix. + * @param angleInRadians - The angle by which to rotate (in radians). + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The rotated matrix. + */ +const rotateZ = rotate; + /** * Creates a 3-by-3 matrix which scales in each dimension by an amount given by - * the corresponding entry in the given vector; assumes the vector has three + * the corresponding entry in the given vector; assumes the vector has two * entries. * @param v - A vector of * 2 entries specifying the factor by which to scale in each dimension. @@ -683,7 +812,7 @@ function scaling(v: Vec2Arg, dst?: T) { /** * Scales the given 3-by-3 matrix in each dimension by an amount * given by the corresponding entry in the given vector; assumes the vector has - * three entries. + * two entries. * @param m - The matrix to be modified. * @param v - A vector of 2 entries specifying the * factor by which to scale in each dimension. @@ -714,7 +843,58 @@ function scale(m: Mat3Arg, v: Vec2Arg, dst?: T) { } /** - * Creates a 3-by-3 matrix which scales uniformly in each dimension + * Creates a 3-by-3 matrix which scales in each dimension by an amount given by + * the corresponding entry in the given vector; assumes the vector has three + * entries. + * @param v - A vector of + * 3 entries specifying the factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ +function scaling3D(v: Vec3Arg, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; + newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; + newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; + + return newDst; +} + +/** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given by the corresponding entry in the given vector; assumes the vector has + * three entries. + * @param m - The matrix to be modified. + * @param v - A vector of 3 entries specifying the + * factor by which to scale in each dimension. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ +function scale3D(m: Mat3Arg, v: Vec3Arg, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + const v0 = v[0]; + const v1 = v[1]; + const v2 = v[2]; + + newDst[ 0] = v0 * m[0 * 4 + 0]; + newDst[ 1] = v0 * m[0 * 4 + 1]; + newDst[ 2] = v0 * m[0 * 4 + 2]; + + newDst[ 4] = v1 * m[1 * 4 + 0]; + newDst[ 5] = v1 * m[1 * 4 + 1]; + newDst[ 6] = v1 * m[1 * 4 + 2]; + + newDst[ 8] = v2 * m[2 * 4 + 0]; + newDst[ 9] = v2 * m[2 * 4 + 1]; + newDst[10] = v2 * m[2 * 4 + 2]; + + return newDst; +} + +/** + * Creates a 3-by-3 matrix which scales uniformly in the X and Y dimensions * @param s - Amount to scale * @param dst - matrix to hold result. If not passed a new one is created. * @returns The scaling matrix. @@ -730,7 +910,7 @@ function uniformScaling(s: number, dst?: T) { } /** - * Scales the given 3-by-3 matrix in each dimension by an amount + * Scales the given 3-by-3 matrix in the X and Y dimension by an amount * given. * @param m - The matrix to be modified. * @param s - Amount to scale. @@ -757,6 +937,48 @@ function uniformScale(m: Mat3Arg, s: number, dst?: return newDst; } +/** + * Creates a 3-by-3 matrix which scales uniformly in each dimension + * @param s - Amount to scale + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaling matrix. + */ +function uniformScaling3D(s: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; + newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; + newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; + + return newDst; +} + +/** + * Scales the given 3-by-3 matrix in each dimension by an amount + * given. + * @param m - The matrix to be modified. + * @param s - Amount to scale. + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The scaled matrix. + */ +function uniformScale3D(m: Mat3Arg, s: number, dst?: T) { + const newDst = (dst ?? new Ctor(12)) as T; + + newDst[ 0] = s * m[0 * 4 + 0]; + newDst[ 1] = s * m[0 * 4 + 1]; + newDst[ 2] = s * m[0 * 4 + 2]; + + newDst[ 4] = s * m[1 * 4 + 0]; + newDst[ 5] = s * m[1 * 4 + 1]; + newDst[ 6] = s * m[1 * 4 + 2]; + + newDst[ 8] = s * m[2 * 4 + 0]; + newDst[ 9] = s * m[2 * 4 + 1]; + newDst[10] = s * m[2 * 4 + 2]; + + return newDst; +} + return { clone, create, @@ -784,10 +1006,20 @@ return { translate, rotation, rotate, + rotationX, + rotateX, + rotationY, + rotateY, + rotationZ, + rotateZ, scaling, scale, uniformScaling, uniformScale, + scaling3D, + scale3D, + uniformScaling3D, + uniformScale3D, }; } diff --git a/test/tests/mat3-test.js b/test/tests/mat3-test.js index 3ccde0c..30691d2 100644 --- a/test/tests/mat3-test.js +++ b/test/tests/mat3-test.js @@ -448,6 +448,78 @@ function check(mat3, Type) { }, expected); }); + it('should make rotationX matrix', () => { + const angle = 1.23; + const c = Math.cos(angle); + const s = Math.sin(angle); + const expected = [ + 1, 0, 0, 0, + 0, c, s, 0, + 0, -s, c, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotationX(angle, newDst); + }, expected); + }); + + it('should rotateX', () => { + const angle = 1.23; + // switch to Array type to keep precision high for expected + const expected = mat3n.multiply(m, mat3.rotationX(angle)); + + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotateX(m, angle, newDst); + }, expected); + }); + + it('should make rotationY matrix', () => { + const angle = 1.23; + const c = Math.cos(angle); + const s = Math.sin(angle); + const expected = [ + c, 0, -s, 0, + 0, 1, 0, 0, + s, 0, c, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotationY(angle, newDst); + }, expected); + }); + + it('should rotateY', () => { + const angle = 1.23; + // switch to Array type to keep precision high for expected + const expected = mat3n.multiply(m, mat3.rotationY(angle)); + + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotateY(m, angle, newDst); + }, expected); + }); + + it('should make rotationZ matrix', () => { + const angle = 1.23; + const c = Math.cos(angle); + const s = Math.sin(angle); + const expected = [ + c, s, 0, 0, + -s, c, 0, 0, + 0, 0, 1, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotationZ(angle, newDst); + }, expected); + }); + + it('should rotateZ', () => { + const angle = 1.23; + // switch to Array type to keep precision high for expected + const expected = mat3n.multiply(m, mat3.rotationZ(angle)); + + testMat3WithAndWithoutDest((newDst) => { + return mat3.rotateZ(m, angle, newDst); + }, expected); + }); + it('should make scaling matrix', () => { const expected = [ 2, 0, 0, 0, @@ -470,6 +542,28 @@ function check(mat3, Type) { }, expected); }); + it('should make 3D scaling matrix', () => { + const expected = [ + 2, 0, 0, 0, + 0, 3, 0, 0, + 0, 0, 4, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.scaling3D([2, 3, 4], newDst); + }, expected); + }); + + it('should scale 3D', () => { + const expected = [ + 0, 2, 4, 0, + 12, 15, 18, 0, + 32, 36, 40, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.scale3D(m, [2, 3, 4], newDst); + }, expected); + }); + it('should make uniform scaling matrix', () => { const expected = [ 2, 0, 0, 0, @@ -492,6 +586,28 @@ function check(mat3, Type) { }, expected); }); + it('should make uniform scaling 3D matrix', () => { + const expected = [ + 2, 0, 0, 0, + 0, 2, 0, 0, + 0, 0, 2, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.uniformScaling3D(2, newDst); + }, expected); + }); + + it('should uniformly scale 3D', () => { + const expected = [ + 0, 2, 4, 0, + 8, 10, 12, 0, + 16, 18, 20, 0, + ]; + testMat3WithAndWithoutDest((newDst) => { + return mat3.uniformScale3D(m, 2, newDst); + }, expected); + }); + it('should make a mat3 from mat4', () => { const expected = [ 1, 2, 3, 0,