From f4a6b214c3237de4c694ecf9fb59af314a276004 Mon Sep 17 00:00:00 2001 From: greggman Date: Tue, 14 May 2024 14:54:45 +0000 Subject: [PATCH] =?UTF-8?q?Deploying=20to=20gh-pages=20from=20@=20greggman?= =?UTF-8?q?/wgpu-matrix@023174b0de565b967a9a198fceac3f8dc1f7c086=20?= =?UTF-8?q?=F0=9F=9A=80?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- dist/2.x/mat4-impl.d.ts | 40 ++++++ dist/2.x/wgpu-matrix.js | 105 +++++++++++++- dist/2.x/wgpu-matrix.js.map | 2 +- dist/2.x/wgpu-matrix.min.js | 31 +++-- dist/2.x/wgpu-matrix.module.js | 105 +++++++++++++- dist/2.x/wgpu-matrix.module.js.map | 2 +- docs/assets/navigation.js | 2 +- docs/assets/search.js | 2 +- docs/functions/mat4.frustumReverseZ.html | 17 +++ docs/functions/mat4.perspectiveReverseZ.html | 19 +++ docs/modules/mat4.html | 2 + package-lock.json | 4 +- package.json | 2 +- src/mat4-impl.ts | 112 ++++++++++++++- test/tests/mat4-test.js | 139 +++++++++++++++++++ 15 files changed, 551 insertions(+), 33 deletions(-) create mode 100644 docs/functions/mat4.frustumReverseZ.html create mode 100644 docs/functions/mat4.perspectiveReverseZ.html diff --git a/dist/2.x/mat4-impl.d.ts b/dist/2.x/mat4-impl.d.ts index 2f16fd3..63d25fb 100644 --- a/dist/2.x/mat4-impl.d.ts +++ b/dist/2.x/mat4-impl.d.ts @@ -242,6 +242,27 @@ export declare function getScaling(m: Mat4, dst?: Vec3): Vec3; * @returns The perspective matrix. */ export declare function perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: Mat4): Mat4; +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height + * of the frustum, the aspect ratio, and the near and far clipping planes. The + * arguments define a frustum extending in the negative z direction. The given + * angle is the vertical angle of the frustum, and the horizontal angle is + * determined to produce the given aspect ratio. The arguments near and far are + * the distances to the near and far clipping planes. Note that near and far + * are not z coordinates, but rather they are distances along the negative + * z-axis. The matrix generated sends the viewing frustum to the unit box. + * We assume a unit box extending from -1 to 1 in the x and y dimensions and + * from 1 (at -zNear) to 0 (at -zFar) in the z dimension. + * + * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians). + * @param aspect - The aspect ratio width / height. + * @param zNear - The depth (negative z coordinate) + * of the near clipping plane. + * @param zFar - The depth (negative z coordinate) + * of the far clipping plane. (default = Infinity) + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The perspective matrix. + */ export declare function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar?: number, dst?: Mat4): Mat4; /** * Computes a 4-by-4 orthogonal transformation matrix that transforms from * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y @@ -277,6 +298,25 @@ export declare function ortho(left: number, right: number, bottom: number, top: * @returns The perspective projection matrix. */ export declare function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4; +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right, + * top, bottom, near and far clipping planes. The arguments define a frustum + * extending in the negative z direction. The arguments near and far are the + * distances to the near and far clipping planes. Note that near and far are not + * z coordinates, but rather they are distances along the negative z-axis. The + * matrix generated sends the viewing frustum to the unit box. We assume a unit + * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z + * dimension. + * @param left - The x coordinate of the left plane of the box. + * @param right - The x coordinate of the right plane of the box. + * @param bottom - The y coordinate of the bottom plane of the box. + * @param top - The y coordinate of the right plane of the box. + * @param near - The negative z coordinate of the near plane of the box. + * @param far - The negative z coordinate of the far plane of the box. + * @param dst - Output matrix. If not passed a new one is created. + * @returns The perspective projection matrix. + */ +export declare function frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far?: number, dst?: Mat4): Mat4; /** * Computes a 4-by-4 aim transformation. * diff --git a/dist/2.x/wgpu-matrix.js b/dist/2.x/wgpu-matrix.js index 85066d1..2f7dc21 100644 --- a/dist/2.x/wgpu-matrix.js +++ b/dist/2.x/wgpu-matrix.js @@ -1,4 +1,4 @@ -/* wgpu-matrix@2.8.3, license MIT */ +/* wgpu-matrix@2.9.0, license MIT */ (function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) : typeof define === 'function' && define.amd ? define(['exports'], factory) : @@ -3345,13 +3345,61 @@ dst[12] = 0; dst[13] = 0; dst[15] = 0; - if (zFar === Infinity) { + if (Number.isFinite(zFar)) { + const rangeInv = 1 / (zNear - zFar); + dst[10] = zFar * rangeInv; + dst[14] = zFar * zNear * rangeInv; + } + else { dst[10] = -1; dst[14] = -zNear; } + return dst; + } + /** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height + * of the frustum, the aspect ratio, and the near and far clipping planes. The + * arguments define a frustum extending in the negative z direction. The given + * angle is the vertical angle of the frustum, and the horizontal angle is + * determined to produce the given aspect ratio. The arguments near and far are + * the distances to the near and far clipping planes. Note that near and far + * are not z coordinates, but rather they are distances along the negative + * z-axis. The matrix generated sends the viewing frustum to the unit box. + * We assume a unit box extending from -1 to 1 in the x and y dimensions and + * from 1 (at -zNear) to 0 (at -zFar) in the z dimension. + * + * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians). + * @param aspect - The aspect ratio width / height. + * @param zNear - The depth (negative z coordinate) + * of the near clipping plane. + * @param zFar - The depth (negative z coordinate) + * of the far clipping plane. (default = Infinity) + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The perspective matrix. + */ function perspectiveReverseZ(fieldOfViewYInRadians, aspect, zNear, zFar = Infinity, dst) { + dst = dst || new MatType(16); + const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5); + dst[0] = f / aspect; + dst[1] = 0; + dst[2] = 0; + dst[3] = 0; + dst[4] = 0; + dst[5] = f; + dst[6] = 0; + dst[7] = 0; + dst[8] = 0; + dst[9] = 0; + dst[11] = -1; + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + if (zFar === Infinity) { + dst[10] = 0; + dst[14] = zNear; + } else { - const rangeInv = 1 / (zNear - zFar); - dst[10] = zFar * rangeInv; + const rangeInv = 1 / (zFar - zNear); + dst[10] = zNear * rangeInv; dst[14] = zFar * zNear * rangeInv; } return dst; @@ -3432,6 +3480,53 @@ dst[15] = 0; return dst; } + /** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right, + * top, bottom, near and far clipping planes. The arguments define a frustum + * extending in the negative z direction. The arguments near and far are the + * distances to the near and far clipping planes. Note that near and far are not + * z coordinates, but rather they are distances along the negative z-axis. The + * matrix generated sends the viewing frustum to the unit box. We assume a unit + * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z + * dimension. + * @param left - The x coordinate of the left plane of the box. + * @param right - The x coordinate of the right plane of the box. + * @param bottom - The y coordinate of the bottom plane of the box. + * @param top - The y coordinate of the right plane of the box. + * @param near - The negative z coordinate of the near plane of the box. + * @param far - The negative z coordinate of the far plane of the box. + * @param dst - Output matrix. If not passed a new one is created. + * @returns The perspective projection matrix. + */ + function frustumReverseZ(left, right, bottom, top, near, far = Infinity, dst) { + dst = dst || new MatType(16); + const dx = (right - left); + const dy = (top - bottom); + dst[0] = 2 * near / dx; + dst[1] = 0; + dst[2] = 0; + dst[3] = 0; + dst[4] = 0; + dst[5] = 2 * near / dy; + dst[6] = 0; + dst[7] = 0; + dst[8] = (left + right) / dx; + dst[9] = (top + bottom) / dy; + dst[11] = -1; + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + if (far === Infinity) { + dst[10] = 0; + dst[14] = near; + } + else { + const rangeInv = 1 / (far - near); + dst[10] = near * rangeInv; + dst[14] = far * near * rangeInv; + } + return dst; + } let xAxis; let yAxis; let zAxis; @@ -4099,6 +4194,7 @@ fromMat3: fromMat3, fromQuat: fromQuat, frustum: frustum, + frustumReverseZ: frustumReverseZ, getAxis: getAxis, getScaling: getScaling, getTranslation: getTranslation, @@ -4111,6 +4207,7 @@ negate: negate$1, ortho: ortho, perspective: perspective, + perspectiveReverseZ: perspectiveReverseZ, rotate: rotate, rotateX: rotateX$1, rotateY: rotateY$1, diff --git a/dist/2.x/wgpu-matrix.js.map b/dist/2.x/wgpu-matrix.js.map index 4a2e1f0..3c9a94e 100644 --- a/dist/2.x/wgpu-matrix.js.map +++ b/dist/2.x/wgpu-matrix.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/utils.ts","../../../src/vec2.ts","../../../src/vec3.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat.ts","../../../src/quat-impl.ts","../../../src/vec4.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/*\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 */\n\n/**\n * A JavaScript array with 2 values, Float32Array with 2 values, or a Float64Array with 2 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec2.setDefaultType}.\n */\nexport type Vec2 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec2 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new Vec2. In other words you can do this\n *\n * const v = vec2.cross(v1, v2); // Creates a new Vec2 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec2.create();\n * vec2.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 * vec2.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec2 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec2\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec2\n */\nexport function setDefaultType(ctor: new (n: number) => Vec2) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Vec2Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `vec2.create` is usually used\n * to create a Vec2 to be filled out as in\n *\n * ```\n * const sum = vec2.create();\n * vec2.add(v1, v2, sum);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nexport function create(x = 0, y = 0): Vec2 {\n const dst = new VecType(2);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n }\n }\n return dst;\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\n/**\n * A JavaScript array with 3 values, Float32Array with 3 values, or a Float64Array with 3 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec3.setDefaultType}.\n */\nexport type Vec3 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec3 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new `Vec3`. In other words you can do this\n *\n * const v = vec3.cross(v1, v2); // Creates a new Vec3 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec3.create();\n * vec3.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 * vec3.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec3 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec3\n */\nexport function setDefaultType(ctor: new (n: number) => Vec3) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number): Vec3 {\n const dst = new VecType(3);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n }\n }\n }\n return dst;\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 { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Vec2, create, setDefaultType, VecType } from './vec2';\nimport { Vec3, VecType as Vec3Type } from './vec3';\n\nexport default Vec2;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = x;\n dst[1] = y;\n\n return dst;\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 */\nexport function ceil(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n\n return dst;\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 */\nexport function floor(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n\n return dst;\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 */\nexport function round(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n\n return dst;\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 */\nexport function clamp(v: Vec2, min = 0, max = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n\n return dst;\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 */\nexport function add(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n\n return dst;\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 */\nexport function addScaled(a: Vec2, b: Vec2, scale: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec2, b: Vec2): 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 */\nexport function subtract(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec2, b: Vec2): 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 */\nexport function equals(a: Vec2, b: Vec2): 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 */\nexport function lerp(a: Vec2, b: Vec2, t: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n\n return dst;\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 */\nexport function lerpV(a: Vec2, b: Vec2, t: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return dst;\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 */\nexport function max(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n\n return dst;\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 */\nexport function min(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec2, b: Vec2, dst?: Vec3): Vec3 {\n dst = dst || new Vec3Type(3);\n const z = a[0] * b[1] - a[1] * b[0];\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = z;\n\n return dst;\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 */\nexport function dot(a: Vec2, b: Vec2): 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 */\nexport function length(v: Vec2): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec2): 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 */\nexport const 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 */\nexport function distance(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function normalize(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n\n return dst;\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 */\nexport function copy(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0];\n dst[1] = v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const angle = Math.random() * 2 * Math.PI;\n dst[0] = Math.cos(angle) * scale;\n dst[1] = Math.sin(angle) * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 0;\n dst[1] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec2, m: Mat4, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = x * m[0] + y * m[4] + m[12];\n dst[1] = x * m[1] + y * m[5] + m[13];\n\n return dst;\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 */\nexport function transformMat3(v: Vec2, m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = m[0] * x + m[4] * y + m[8];\n dst[1] = m[1] * x + m[5] * y + m[9];\n\n return dst;\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 */\nexport function rotate(a: Vec2, b: Vec2, rad: number, dst?: Vec2) {\n dst = dst || new VecType(2);\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 dst[0] = p0 * cosC - p1 * sinC + b[0];\n dst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return dst;\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 */\nexport function setLength(a: Vec2, len: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec2, maxLen: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n return lerp(a, b, 0.5, dst);\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 { Quat } from './quat';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport Vec2, * as vec2 from './vec2-impl';\n\nexport default Mat3;\n\nexport type Mat3LikeCtor = new (n: number) => Mat3;\n\n/**\n * 3x3 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 = mat3.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat3.create();\n * mat3.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 = mat3.identity();\n * const trans = mat3.translation([1, 2, 3]);\n * mat3.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\nlet MatType: Mat3LikeCtor = Float32Array;\n\n// This mess is because with Mat3 we have 3 unused elements.\n// For Float32Array and Float64Array that's not an issue\n// but for Array it's troublesome\nconst ctorMap = new Map Mat3>([\n [Float32Array, () => new Float32Array(12)],\n [Float64Array, () => new Float64Array(12)],\n [Array, () => new Array(12).fill(0)],\n]);\nlet newMat3: () => Mat3 = ctorMap.get(Float32Array)!;\n\n/**\n * Sets the type this library creates for a Mat3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat3\n */\nexport function setDefaultType(ctor: new (n: number) => Mat3) {\n const oldType = MatType;\n MatType = ctor;\n newMat3 = ctorMap.get(ctor)!;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Mat3Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat3.create` is usually used\n * to create a Mat3 to be filled out as in\n *\n * ```\n * const m = mat3.create();\n * mat3.perspective(fov, aspect, near, far, m);\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 */\nexport function create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number): Mat3 {\n const dst = newMat3();\n // to make the array homogenous\n dst[3] = 0;\n dst[7] = 0;\n dst[11] = 0;\n\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[4] = v3;\n if (v4 !== undefined) {\n dst[5] = v4;\n if (v5 !== undefined) {\n dst[6] = v5;\n if (v6 !== undefined) {\n dst[8] = v6;\n if (v7 !== undefined) {\n dst[9] = v7;\n if (v8 !== undefined) {\n dst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return dst;\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 */\nexport function set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: Mat3) {\n dst = dst || newMat3();\n\n dst[0] = v0; dst[1] = v1; dst[ 2] = v2; dst[ 3] = 0;\n dst[4] = v3; dst[5] = v4; dst[ 6] = v5; dst[ 7] = 0;\n dst[8] = v6; dst[9] = v7; dst[10] = v8; dst[11] = 0;\n\n return dst;\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 */\nexport function fromMat4(m4: Mat4, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n dst[0] = m4[0]; dst[1] = m4[1]; dst[ 2] = m4[ 2]; dst[ 3] = 0;\n dst[4] = m4[4]; dst[5] = m4[5]; dst[ 6] = m4[ 6]; dst[ 7] = 0;\n dst[8] = m4[8]; dst[9] = m4[9]; dst[10] = m4[10]; dst[11] = 0;\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n\n return dst;\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 */\nexport function negate(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10];\n\n return dst;\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 */\nexport function copy(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat3, b: Mat3): 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 */\nexport function equals(a: Mat3, b: Mat3): 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 */\nexport function identity(dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22;\n\n return dst;\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 */\nexport function inverse(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = b01 * invDet;\n dst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n dst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n dst[ 4] = b11 * invDet;\n dst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n dst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n dst[ 8] = b21 * invDet;\n dst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n dst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat3): 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 */\nexport const 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 */\nexport function multiply(a: Mat3, b: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n }\n dst[ 8] = v[0];\n dst[ 9] = v[1];\n dst[10] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n dst[0] = m[8];\n dst[1] = m[9];\n return dst;\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 */\nexport function getAxis(m: Mat3, axis: number, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n return dst;\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 */\nexport function setAxis(m: Mat3, v: Vec2, axis: number, dst?: Mat3): Mat3 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n return dst;\n}\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 */\nexport function getScaling(m: Mat3, dst?: Vec2): Vec2 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy);\n dst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return dst;\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 */\nexport function translation(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = v[0]; dst[ 9] = v[1]; dst[10] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n }\n\n dst[ 8] = m00 * v0 + m10 * v1 + m20;\n dst[ 9] = m01 * v0 + m11 * v1 + m21;\n dst[10] = m02 * v0 + m12 * v1 + m22;\n\n return dst;\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 */\nexport function rotation(angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function rotate(m: Mat3, angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function scaling(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const v0 = v[0];\n const v1 = v[1];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat3, s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 { Vec3, create, setDefaultType, VecType } from './vec3';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\n\nexport default Vec3;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n\n return dst;\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 */\nexport function ceil(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n\n return dst;\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 */\nexport function floor(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n\n return dst;\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 */\nexport function round(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n\n return dst;\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 */\nexport function clamp(v: Vec3, min = 0, max = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n\n return dst;\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 */\nexport function add(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n\n return dst;\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 */\nexport function addScaled(a: Vec3, b: Vec3, scale: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec3, b: Vec3): 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 */\nexport function subtract(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec3, b: Vec3): 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 */\nexport function equals(a: Vec3, b: Vec3): 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 */\nexport function lerp(a: Vec3, b: Vec3, t: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n\n return dst;\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 */\nexport function lerpV(a: Vec3, b: Vec3, t: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return dst;\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 */\nexport function max(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n\n return dst;\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 */\nexport function min(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n dst[0] = a[1] * b[2] - a[2] * b[1];\n dst[1] = t1;\n dst[2] = t2;\n\n return dst;\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 */\nexport function dot(a: Vec3, b: Vec3): 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 */\nexport function length(v: Vec3): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec3): 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 */\nexport const 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 */\nexport function distance(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function normalize(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n\n return dst;\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 */\nexport function negate(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n\n return dst;\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 */\nexport function copy(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = Math.cos(angle) * zScale;\n dst[1] = Math.sin(angle) * zScale;\n dst[2] = z * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n dst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n dst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return dst;\n}\n\n/**\n * Transform vec4 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 */\nexport function transformMat4Upper3x3(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return dst;\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 */\nexport function transformMat3(v: Vec3, m: Mat3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n dst[0] = x * m[0] + y * m[4] + z * m[8];\n dst[1] = x * m[1] + y * m[5] + z * m[9];\n dst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return dst;\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 */\nexport function transformQuat(v: Vec3, q: Quat, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n dst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n dst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec3) {\n dst = dst || new VecType(3);\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function getScaling(m: Mat4, dst: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return dst;\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 */\nexport function rotateX(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateY(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateZ(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function setLength(a: Vec3, len: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec3, maxLen: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n return lerp(a, b, 0.5, dst);\n}\n","\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\nimport Vec3, * as vec3 from './vec3-impl';\nimport * as utils from './utils';\n\nexport default Mat4;\n\nexport type Mat4LikeCtor = new (n: number) => Mat4;\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 */\nlet MatType: Mat4LikeCtor = Float32Array;\n\n/**\n * Sets the type this library creates for a Mat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat4\n */\nexport function setDefaultType(ctor: new (n: number) => Mat4) {\n const oldType = MatType;\n MatType = ctor;\n return oldType;\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 * Note: a consequence of the implementation is if your Mat4Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat4.create` is usually used\n * to create a Mat4 to be filled out as in\n *\n * ```\n * const m = mat4.create();\n * mat4.perspective(fov, aspect, near, far, m);\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 */\nexport function 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): Mat4 {\n const dst = new MatType(16);\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[3] = v3;\n if (v4 !== undefined) {\n dst[4] = v4;\n if (v5 !== undefined) {\n dst[5] = v5;\n if (v6 !== undefined) {\n dst[6] = v6;\n if (v7 !== undefined) {\n dst[7] = v7;\n if (v8 !== undefined) {\n dst[8] = v8;\n if (v9 !== undefined) {\n dst[9] = v9;\n if (v10 !== undefined) {\n dst[10] = v10;\n if (v11 !== undefined) {\n dst[11] = v11;\n if (v12 !== undefined) {\n dst[12] = v12;\n if (v13 !== undefined) {\n dst[13] = v13;\n if (v14 !== undefined) {\n dst[14] = v14;\n if (v15 !== undefined) {\n dst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return dst;\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 */\nexport function 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?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v0; dst[ 1] = v1; dst[ 2] = v2; dst[ 3] = v3;\n dst[ 4] = v4; dst[ 5] = v5; dst[ 6] = v6; dst[ 7] = v7;\n dst[ 8] = v8; dst[ 9] = v9; dst[10] = v10; dst[11] = v11;\n dst[12] = v12; dst[13] = v13; dst[14] = v14; dst[15] = v15;\n\n return dst;\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 */\nexport function fromMat3(m3: Mat3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m3[0]; dst[ 1] = m3[1]; dst[ 2] = m3[ 2]; dst[ 3] = 0;\n dst[ 4] = m3[4]; dst[ 5] = m3[5]; dst[ 6] = m3[ 6]; dst[ 7] = 0;\n dst[ 8] = m3[8]; dst[ 9] = m3[9]; dst[10] = m3[10]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function negate(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2]; dst[ 3] = -m[ 3];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6]; dst[ 7] = -m[ 7];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10]; dst[11] = -m[11];\n dst[12] = -m[12]; dst[13] = -m[13]; dst[14] = -m[14]; dst[15] = -m[15];\n\n return dst;\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 */\nexport function copy(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2]; dst[ 3] = m[ 3];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6]; dst[ 7] = m[ 7];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10]; dst[11] = m[11];\n dst[12] = m[12]; dst[13] = m[13]; dst[14] = m[14]; dst[15] = m[15];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat4, b: Mat4): 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 */\nexport function equals(a: Mat4, b: Mat4): 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 */\nexport function identity(dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20; dst[ 3] = m30;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21; dst[ 7] = m31;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22; dst[11] = m32;\n dst[12] = m03; dst[13] = m13; dst[14] = m23; dst[15] = m33;\n\n return dst;\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 */\nexport function inverse(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = d * t0;\n dst[ 1] = d * t1;\n dst[ 2] = d * t2;\n dst[ 3] = d * t3;\n dst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n dst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n dst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n dst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n dst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n dst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n dst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n dst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n dst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n dst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n dst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n dst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat4): 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 */\nexport const 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 */\nexport function multiply(a: Mat4, b: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n dst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n dst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n dst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n dst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n dst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n dst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n dst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 3] = a[ 3];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n dst[ 7] = a[ 7];\n dst[ 8] = a[ 8];\n dst[ 9] = a[ 9];\n dst[10] = a[10];\n dst[11] = a[11];\n }\n dst[12] = v[0];\n dst[13] = v[1];\n dst[14] = v[2];\n dst[15] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function setAxis(m: Mat4, v: Vec3, axis: number, dst: Mat4): Mat4 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n dst[off + 2] = v[2];\n return dst;\n}\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 */\nexport function getScaling(m: Mat4, dst?: Vec3): Vec3 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return dst;\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 */\nexport function perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n dst[0] = f / aspect;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = f;\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (zFar === Infinity) {\n dst[10] = -1;\n dst[14] = -zNear;\n } else {\n const rangeInv = 1 / (zNear - zFar);\n dst[10] = zFar * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n }\n\n return dst;\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 */\nexport function ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[0] = 2 / (right - left);\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = 2 / (top - bottom);\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[10] = 1 / (near - far);\n dst[11] = 0;\n\n dst[12] = (right + left) / (left - right);\n dst[13] = (top + bottom) / (bottom - top);\n dst[14] = near / (near - far);\n dst[15] = 1;\n\n return dst;\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 */\nexport function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[10] = far / dz;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = near * far / dz;\n dst[15] = 0;\n\n return dst;\n}\n\nlet xAxis: Vec3;\nlet yAxis: Vec3;\nlet zAxis: Vec3;\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 */\nexport function aim(position: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = position[0]; dst[13] = position[1]; dst[14] = position[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function cameraAim(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = eye[0]; dst[13] = eye[1]; dst[14] = eye[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function lookAt(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = yAxis[0]; dst[ 2] = zAxis[0]; dst[ 3] = 0;\n dst[ 4] = xAxis[1]; dst[ 5] = yAxis[1]; dst[ 6] = zAxis[1]; dst[ 7] = 0;\n dst[ 8] = xAxis[2]; dst[ 9] = yAxis[2]; dst[10] = zAxis[2]; dst[11] = 0;\n\n dst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n dst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n dst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n dst[15] = 1;\n\n return dst;\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 */\nexport function translation(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = v[0]; dst[13] = v[1]; dst[14] = v[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 3] = m03;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n dst[ 7] = m13;\n dst[ 8] = m20;\n dst[ 9] = m21;\n dst[10] = m22;\n dst[11] = m23;\n }\n\n dst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n dst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n dst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n dst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return dst;\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 */\nexport function rotationX(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = c; dst[ 6] = s; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = -s; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateX(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[4] = c * m10 + s * m20;\n dst[5] = c * m11 + s * m21;\n dst[6] = c * m12 + s * m22;\n dst[7] = c * m13 + s * m23;\n dst[8] = c * m20 - s * m10;\n dst[9] = c * m21 - s * m11;\n dst[10] = c * m22 - s * m12;\n dst[11] = c * m23 - s * m13;\n\n if (m !== dst) {\n dst[ 0] = m[ 0];\n dst[ 1] = m[ 1];\n dst[ 2] = m[ 2];\n dst[ 3] = m[ 3];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationY(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = 0; dst[ 2] = -s; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = s; dst[ 9] = 0; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateY(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 - s * m20;\n dst[ 1] = c * m01 - s * m21;\n dst[ 2] = c * m02 - s * m22;\n dst[ 3] = c * m03 - s * m23;\n dst[ 8] = c * m20 + s * m00;\n dst[ 9] = c * m21 + s * m01;\n dst[10] = c * m22 + s * m02;\n dst[11] = c * m23 + s * m03;\n\n if (m !== dst) {\n dst[ 4] = m[ 4];\n dst[ 5] = m[ 5];\n dst[ 6] = m[ 6];\n dst[ 7] = m[ 7];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationZ(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateZ(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n dst[ 3] = c * m03 + s * m13;\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n dst[ 7] = c * m13 - s * m03;\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n dst[11] = m[11];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function axisRotation(axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = xx + (1 - xx) * c;\n dst[ 1] = x * y * oneMinusCosine + z * s;\n dst[ 2] = x * z * oneMinusCosine - y * s;\n dst[ 3] = 0;\n dst[ 4] = x * y * oneMinusCosine - z * s;\n dst[ 5] = yy + (1 - yy) * c;\n dst[ 6] = y * z * oneMinusCosine + x * s;\n dst[ 7] = 0;\n dst[ 8] = x * z * oneMinusCosine + y * s;\n dst[ 9] = y * z * oneMinusCosine - x * s;\n dst[10] = zz + (1 - zz) * c;\n dst[11] = 0;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = 0;\n dst[15] = 1;\n\n return dst;\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 */\nexport const 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 */\nexport function axisRotate(m: Mat4, axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n dst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n dst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n dst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n dst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n dst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n dst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n dst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n dst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n dst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n dst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n dst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport const 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 */\nexport function scaling(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = v[2]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n dst[ 3] = v0 * m[0 * 4 + 3];\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n dst[ 7] = v1 * m[1 * 4 + 3];\n dst[ 8] = v2 * m[2 * 4 + 0];\n dst[ 9] = v2 * m[2 * 4 + 1];\n dst[10] = v2 * m[2 * 4 + 2];\n dst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = s; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat4, s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n dst[ 3] = s * m[0 * 4 + 3];\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n dst[ 7] = s * m[1 * 4 + 3];\n dst[ 8] = s * m[2 * 4 + 0];\n dst[ 9] = s * m[2 * 4 + 1];\n dst[10] = s * m[2 * 4 + 2];\n dst[11] = s * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link quat.setDefaultType}.\n */\nexport type Quat = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let QuatType: new (n: number) => Quat = Float32Array;\n\n/**\n * Sets the type this library creates for a Quat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Quat4\n */\nexport function setDefaultType(ctor: new (n: number) => Quat) {\n const oldType = QuatType;\n QuatType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Quat {\n const dst = new QuatType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Quat, create, setDefaultType, QuatType } from './quat';\nimport { Mat3 } from './mat3.js';\nimport { Mat4 } from './mat4.js';\nimport { Vec3 } from './vec3.js';\nimport * as vec3 from './vec3-impl.js';\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\nexport default Quat;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Quat) {\n dst = dst || new QuatType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 **/\nexport function fromAxisAngle(axis: Vec3, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n dst[0] = s * axis[0];\n dst[1] = s * axis[1];\n dst[2] = s * axis[2];\n dst[3] = Math.cos(halfAngle);\n\n return dst;\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 */\nexport function toAxisAngle(q: Quat, dst?: Vec3): { angle: number, axis: Vec3 } {\n dst = dst || vec3.create(4);\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n dst[0] = q[0] / s;\n dst[1] = q[1] / s;\n dst[2] = q[2] / s;\n } else {\n dst[0] = 1;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n return { angle, axis: dst };\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 */\nexport function angle(a: Quat, b: Quat) {\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 */\nexport function multiply(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = ax * bw + aw * bx + ay * bz - az * by;\n dst[1] = ay * bw + aw * by + az * bx - ax * bz;\n dst[2] = az * bw + aw * bz + ax * by - ay * bx;\n dst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return dst;\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 */\nexport const 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 */\nexport function rotateX(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qw * bx;\n dst[1] = qy * bw + qz * bx;\n dst[2] = qz * bw - qy * bx;\n dst[3] = qw * bw - qx * bx;\n\n return dst;\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 */\nexport function rotateY(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw - qz * by;\n dst[1] = qy * bw + qw * by;\n dst[2] = qz * bw + qx * by;\n dst[3] = qw * bw - qy * by;\n\n return dst;\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 */\nexport function rotateZ(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qy * bz;\n dst[1] = qy * bw - qx * bz;\n dst[2] = qz * bw + qw * bz;\n dst[3] = qw * bw - qz * bz;\n\n return dst;\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 */\nexport function slerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = scale0 * ax + scale1 * bx;\n dst[1] = scale0 * ay + scale1 * by;\n dst[2] = scale0 * az + scale1 * bz;\n dst[3] = scale0 * aw + scale1 * bw;\n\n return dst;\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 */\nexport function inverse(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = -a0 * invDot;\n dst[1] = -a1 * invDot;\n dst[2] = -a2 * invDot;\n dst[3] = a3 * invDot;\n\n return dst;\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 */\nexport function conjugate(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = -q[0];\n dst[1] = -q[1];\n dst[2] = -q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport function fromMat(m: Mat3 | Mat4, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n dst[0] = (m[6] - m[9]) * invRoot;\n dst[1] = (m[8] - m[2]) * invRoot;\n dst[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 dst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n dst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n dst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n dst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return dst;\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 */\nexport function fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: Quat) {\n dst = dst || new QuatType(4);\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 dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return dst;\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 */\nexport function copy(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = q[0];\n dst[1] = q[1];\n dst[2] = q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport const 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 */\nexport function add(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function subtract(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function mulScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function dot(a: Quat, b: Quat): 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 */\nexport function lerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nexport function length(v: Quat): 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 */\nexport const 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 */\nexport function lengthSq(v: Quat): 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 */\nexport const 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 */\nexport function normalize(v: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function equalsApproximately(a: Quat, b: Quat): 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 */\nexport function equals(a: Quat, b: Quat): 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 */\nexport function identity(dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n}\n\nlet tempVec3: Vec3;\nlet xUnitVec3: Vec3;\nlet yUnitVec3: Vec3;\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 */\nexport function rotationTo(aUnit: Vec3, bUnit: Vec3, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempVec3 = tempVec3 || vec3.create();\n xUnitVec3 = xUnitVec3 || vec3.create(1, 0, 0);\n yUnitVec3 = yUnitVec3 || vec3.create(0, 1, 0);\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, dst);\n\n return dst;\n } else if (dot > 0.999999) {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n dst[0] = tempVec3[0];\n dst[1] = tempVec3[1];\n dst[2] = tempVec3[2];\n dst[3] = 1 + dot;\n\n return normalize(dst, dst);\n }\n}\n\nlet tempQuat1: Quat;\nlet tempQuat2: Quat;\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 */\nexport function sqlerp(\n a: Quat,\n b: Quat,\n c: Quat,\n d: Quat,\n t: number,\n dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempQuat1 = tempQuat1 || new QuatType(4);\n tempQuat2 = tempQuat2 || new QuatType(4);\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), dst);\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec4.setDefaultType}.\n */\nexport type Vec4 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let VecType: new (n: number) => Vec4 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec4\n */\nexport function setDefaultType(ctor: new (n: number) => Vec4) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Vec4 {\n const dst = new VecType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Vec4, create, setDefaultType, VecType } from './vec4';\nimport { Mat4 } from './mat4';\n\nexport default Vec4;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 */\nexport function ceil(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n dst[3] = Math.ceil(v[3]);\n\n return dst;\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 */\nexport function floor(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n dst[3] = Math.floor(v[3]);\n\n return dst;\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 */\nexport function round(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n dst[3] = Math.round(v[3]);\n\n return dst;\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 */\nexport function clamp(v: Vec4, min = 0, max = 1, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n dst[3] = Math.min(max, Math.max(min, v[3]));\n\n return dst;\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 */\nexport function add(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function addScaled(a: Vec4, b: Vec4, scale: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n dst[3] = a[3] + b[3] * scale;\n\n return dst;\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 */\nexport function subtract(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec4, b: Vec4): 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 */\nexport function equals(a: Vec4, b: Vec4): 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 */\nexport function lerp(a: Vec4, b: Vec4, t: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\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 */\nexport function lerpV(a: Vec4, b: Vec4, t: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n dst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return dst;\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 */\nexport function max(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n dst[3] = Math.max(a[3], b[3]);\n\n return dst;\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 */\nexport function min(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n dst[3] = Math.min(a[3], b[3]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n dst[3] = 1 / v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function dot(a: Vec4, b: Vec4): 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 */\nexport function length(v: Vec4): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec4): 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 */\nexport const 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 */\nexport function distance(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function normalize(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n dst[3] = -v[3];\n\n return dst;\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 */\nexport function copy(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n dst[3] = v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n dst[3] = a[3] * b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n dst[3] = a[3] / b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function zero(dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec4, m: Mat4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n dst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n dst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n dst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n dst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return dst;\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 */\nexport function setLength(a: Vec4, len: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec4, maxLen: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n return lerp(a, b, 0.5, dst);\n}\n","import Mat3, * as mat3 from './mat3-impl';\nimport Mat4, * as mat4 from './mat4-impl';\nimport Quat, * as quat from './quat-impl';\nimport Vec2, * as vec2 from './vec2-impl';\nimport Vec3, * as vec3 from './vec3-impl';\nimport Vec4, * as vec4 from './vec4-impl';\nimport * as utils from './utils';\n\n/**\n * Sets the type this library creates for all types\n *\n * example:\n *\n * ```\n * setDefaultType(Float64Array);\n * ```\n *\n * @param ctor - the constructor for the type. 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/utils.ts","../../../src/vec2.ts","../../../src/vec3.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat.ts","../../../src/quat-impl.ts","../../../src/vec4.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/*\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 */\n\n/**\n * A JavaScript array with 2 values, Float32Array with 2 values, or a Float64Array with 2 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec2.setDefaultType}.\n */\nexport type Vec2 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec2 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new Vec2. In other words you can do this\n *\n * const v = vec2.cross(v1, v2); // Creates a new Vec2 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec2.create();\n * vec2.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 * vec2.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec2 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec2\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec2\n */\nexport function setDefaultType(ctor: new (n: number) => Vec2) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Vec2Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `vec2.create` is usually used\n * to create a Vec2 to be filled out as in\n *\n * ```\n * const sum = vec2.create();\n * vec2.add(v1, v2, sum);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nexport function create(x = 0, y = 0): Vec2 {\n const dst = new VecType(2);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n }\n }\n return dst;\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\n/**\n * A JavaScript array with 3 values, Float32Array with 3 values, or a Float64Array with 3 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec3.setDefaultType}.\n */\nexport type Vec3 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec3 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new `Vec3`. In other words you can do this\n *\n * const v = vec3.cross(v1, v2); // Creates a new Vec3 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec3.create();\n * vec3.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 * vec3.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec3 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec3\n */\nexport function setDefaultType(ctor: new (n: number) => Vec3) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number): Vec3 {\n const dst = new VecType(3);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n }\n }\n }\n return dst;\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 { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Vec2, create, setDefaultType, VecType } from './vec2';\nimport { Vec3, VecType as Vec3Type } from './vec3';\n\nexport default Vec2;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = x;\n dst[1] = y;\n\n return dst;\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 */\nexport function ceil(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n\n return dst;\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 */\nexport function floor(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n\n return dst;\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 */\nexport function round(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n\n return dst;\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 */\nexport function clamp(v: Vec2, min = 0, max = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n\n return dst;\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 */\nexport function add(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n\n return dst;\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 */\nexport function addScaled(a: Vec2, b: Vec2, scale: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec2, b: Vec2): 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 */\nexport function subtract(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec2, b: Vec2): 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 */\nexport function equals(a: Vec2, b: Vec2): 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 */\nexport function lerp(a: Vec2, b: Vec2, t: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n\n return dst;\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 */\nexport function lerpV(a: Vec2, b: Vec2, t: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return dst;\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 */\nexport function max(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n\n return dst;\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 */\nexport function min(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec2, b: Vec2, dst?: Vec3): Vec3 {\n dst = dst || new Vec3Type(3);\n const z = a[0] * b[1] - a[1] * b[0];\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = z;\n\n return dst;\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 */\nexport function dot(a: Vec2, b: Vec2): 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 */\nexport function length(v: Vec2): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec2): 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 */\nexport const 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 */\nexport function distance(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function normalize(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n\n return dst;\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 */\nexport function copy(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0];\n dst[1] = v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const angle = Math.random() * 2 * Math.PI;\n dst[0] = Math.cos(angle) * scale;\n dst[1] = Math.sin(angle) * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 0;\n dst[1] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec2, m: Mat4, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = x * m[0] + y * m[4] + m[12];\n dst[1] = x * m[1] + y * m[5] + m[13];\n\n return dst;\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 */\nexport function transformMat3(v: Vec2, m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = m[0] * x + m[4] * y + m[8];\n dst[1] = m[1] * x + m[5] * y + m[9];\n\n return dst;\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 */\nexport function rotate(a: Vec2, b: Vec2, rad: number, dst?: Vec2) {\n dst = dst || new VecType(2);\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 dst[0] = p0 * cosC - p1 * sinC + b[0];\n dst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return dst;\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 */\nexport function setLength(a: Vec2, len: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec2, maxLen: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n return lerp(a, b, 0.5, dst);\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 { Quat } from './quat';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport Vec2, * as vec2 from './vec2-impl';\n\nexport default Mat3;\n\nexport type Mat3LikeCtor = new (n: number) => Mat3;\n\n/**\n * 3x3 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 = mat3.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat3.create();\n * mat3.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 = mat3.identity();\n * const trans = mat3.translation([1, 2, 3]);\n * mat3.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\nlet MatType: Mat3LikeCtor = Float32Array;\n\n// This mess is because with Mat3 we have 3 unused elements.\n// For Float32Array and Float64Array that's not an issue\n// but for Array it's troublesome\nconst ctorMap = new Map Mat3>([\n [Float32Array, () => new Float32Array(12)],\n [Float64Array, () => new Float64Array(12)],\n [Array, () => new Array(12).fill(0)],\n]);\nlet newMat3: () => Mat3 = ctorMap.get(Float32Array)!;\n\n/**\n * Sets the type this library creates for a Mat3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat3\n */\nexport function setDefaultType(ctor: new (n: number) => Mat3) {\n const oldType = MatType;\n MatType = ctor;\n newMat3 = ctorMap.get(ctor)!;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Mat3Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat3.create` is usually used\n * to create a Mat3 to be filled out as in\n *\n * ```\n * const m = mat3.create();\n * mat3.perspective(fov, aspect, near, far, m);\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 */\nexport function create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number): Mat3 {\n const dst = newMat3();\n // to make the array homogenous\n dst[3] = 0;\n dst[7] = 0;\n dst[11] = 0;\n\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[4] = v3;\n if (v4 !== undefined) {\n dst[5] = v4;\n if (v5 !== undefined) {\n dst[6] = v5;\n if (v6 !== undefined) {\n dst[8] = v6;\n if (v7 !== undefined) {\n dst[9] = v7;\n if (v8 !== undefined) {\n dst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return dst;\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 */\nexport function set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: Mat3) {\n dst = dst || newMat3();\n\n dst[0] = v0; dst[1] = v1; dst[ 2] = v2; dst[ 3] = 0;\n dst[4] = v3; dst[5] = v4; dst[ 6] = v5; dst[ 7] = 0;\n dst[8] = v6; dst[9] = v7; dst[10] = v8; dst[11] = 0;\n\n return dst;\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 */\nexport function fromMat4(m4: Mat4, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n dst[0] = m4[0]; dst[1] = m4[1]; dst[ 2] = m4[ 2]; dst[ 3] = 0;\n dst[4] = m4[4]; dst[5] = m4[5]; dst[ 6] = m4[ 6]; dst[ 7] = 0;\n dst[8] = m4[8]; dst[9] = m4[9]; dst[10] = m4[10]; dst[11] = 0;\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n\n return dst;\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 */\nexport function negate(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10];\n\n return dst;\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 */\nexport function copy(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat3, b: Mat3): 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 */\nexport function equals(a: Mat3, b: Mat3): 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 */\nexport function identity(dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22;\n\n return dst;\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 */\nexport function inverse(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = b01 * invDet;\n dst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n dst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n dst[ 4] = b11 * invDet;\n dst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n dst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n dst[ 8] = b21 * invDet;\n dst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n dst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat3): 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 */\nexport const 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 */\nexport function multiply(a: Mat3, b: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n }\n dst[ 8] = v[0];\n dst[ 9] = v[1];\n dst[10] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n dst[0] = m[8];\n dst[1] = m[9];\n return dst;\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 */\nexport function getAxis(m: Mat3, axis: number, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n return dst;\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 */\nexport function setAxis(m: Mat3, v: Vec2, axis: number, dst?: Mat3): Mat3 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n return dst;\n}\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 */\nexport function getScaling(m: Mat3, dst?: Vec2): Vec2 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy);\n dst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return dst;\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 */\nexport function translation(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = v[0]; dst[ 9] = v[1]; dst[10] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n }\n\n dst[ 8] = m00 * v0 + m10 * v1 + m20;\n dst[ 9] = m01 * v0 + m11 * v1 + m21;\n dst[10] = m02 * v0 + m12 * v1 + m22;\n\n return dst;\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 */\nexport function rotation(angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function rotate(m: Mat3, angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function scaling(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const v0 = v[0];\n const v1 = v[1];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat3, s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 { Vec3, create, setDefaultType, VecType } from './vec3';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\n\nexport default Vec3;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n\n return dst;\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 */\nexport function ceil(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n\n return dst;\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 */\nexport function floor(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n\n return dst;\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 */\nexport function round(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n\n return dst;\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 */\nexport function clamp(v: Vec3, min = 0, max = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n\n return dst;\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 */\nexport function add(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n\n return dst;\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 */\nexport function addScaled(a: Vec3, b: Vec3, scale: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec3, b: Vec3): 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 */\nexport function subtract(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec3, b: Vec3): 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 */\nexport function equals(a: Vec3, b: Vec3): 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 */\nexport function lerp(a: Vec3, b: Vec3, t: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n\n return dst;\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 */\nexport function lerpV(a: Vec3, b: Vec3, t: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return dst;\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 */\nexport function max(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n\n return dst;\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 */\nexport function min(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n dst[0] = a[1] * b[2] - a[2] * b[1];\n dst[1] = t1;\n dst[2] = t2;\n\n return dst;\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 */\nexport function dot(a: Vec3, b: Vec3): 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 */\nexport function length(v: Vec3): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec3): 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 */\nexport const 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 */\nexport function distance(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function normalize(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n\n return dst;\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 */\nexport function negate(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n\n return dst;\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 */\nexport function copy(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = Math.cos(angle) * zScale;\n dst[1] = Math.sin(angle) * zScale;\n dst[2] = z * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n dst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n dst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return dst;\n}\n\n/**\n * Transform vec4 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 */\nexport function transformMat4Upper3x3(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return dst;\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 */\nexport function transformMat3(v: Vec3, m: Mat3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n dst[0] = x * m[0] + y * m[4] + z * m[8];\n dst[1] = x * m[1] + y * m[5] + z * m[9];\n dst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return dst;\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 */\nexport function transformQuat(v: Vec3, q: Quat, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n dst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n dst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec3) {\n dst = dst || new VecType(3);\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function getScaling(m: Mat4, dst: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return dst;\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 */\nexport function rotateX(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateY(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateZ(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function setLength(a: Vec3, len: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec3, maxLen: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n return lerp(a, b, 0.5, dst);\n}\n","\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\nimport Vec3, * as vec3 from './vec3-impl';\nimport * as utils from './utils';\n\nexport default Mat4;\n\nexport type Mat4LikeCtor = new (n: number) => Mat4;\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 */\nlet MatType: Mat4LikeCtor = Float32Array;\n\n/**\n * Sets the type this library creates for a Mat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat4\n */\nexport function setDefaultType(ctor: new (n: number) => Mat4) {\n const oldType = MatType;\n MatType = ctor;\n return oldType;\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 * Note: a consequence of the implementation is if your Mat4Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat4.create` is usually used\n * to create a Mat4 to be filled out as in\n *\n * ```\n * const m = mat4.create();\n * mat4.perspective(fov, aspect, near, far, m);\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 */\nexport function 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): Mat4 {\n const dst = new MatType(16);\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[3] = v3;\n if (v4 !== undefined) {\n dst[4] = v4;\n if (v5 !== undefined) {\n dst[5] = v5;\n if (v6 !== undefined) {\n dst[6] = v6;\n if (v7 !== undefined) {\n dst[7] = v7;\n if (v8 !== undefined) {\n dst[8] = v8;\n if (v9 !== undefined) {\n dst[9] = v9;\n if (v10 !== undefined) {\n dst[10] = v10;\n if (v11 !== undefined) {\n dst[11] = v11;\n if (v12 !== undefined) {\n dst[12] = v12;\n if (v13 !== undefined) {\n dst[13] = v13;\n if (v14 !== undefined) {\n dst[14] = v14;\n if (v15 !== undefined) {\n dst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return dst;\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 */\nexport function 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?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v0; dst[ 1] = v1; dst[ 2] = v2; dst[ 3] = v3;\n dst[ 4] = v4; dst[ 5] = v5; dst[ 6] = v6; dst[ 7] = v7;\n dst[ 8] = v8; dst[ 9] = v9; dst[10] = v10; dst[11] = v11;\n dst[12] = v12; dst[13] = v13; dst[14] = v14; dst[15] = v15;\n\n return dst;\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 */\nexport function fromMat3(m3: Mat3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m3[0]; dst[ 1] = m3[1]; dst[ 2] = m3[ 2]; dst[ 3] = 0;\n dst[ 4] = m3[4]; dst[ 5] = m3[5]; dst[ 6] = m3[ 6]; dst[ 7] = 0;\n dst[ 8] = m3[8]; dst[ 9] = m3[9]; dst[10] = m3[10]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function negate(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2]; dst[ 3] = -m[ 3];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6]; dst[ 7] = -m[ 7];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10]; dst[11] = -m[11];\n dst[12] = -m[12]; dst[13] = -m[13]; dst[14] = -m[14]; dst[15] = -m[15];\n\n return dst;\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 */\nexport function copy(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2]; dst[ 3] = m[ 3];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6]; dst[ 7] = m[ 7];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10]; dst[11] = m[11];\n dst[12] = m[12]; dst[13] = m[13]; dst[14] = m[14]; dst[15] = m[15];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat4, b: Mat4): 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 */\nexport function equals(a: Mat4, b: Mat4): 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 */\nexport function identity(dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20; dst[ 3] = m30;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21; dst[ 7] = m31;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22; dst[11] = m32;\n dst[12] = m03; dst[13] = m13; dst[14] = m23; dst[15] = m33;\n\n return dst;\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 */\nexport function inverse(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = d * t0;\n dst[ 1] = d * t1;\n dst[ 2] = d * t2;\n dst[ 3] = d * t3;\n dst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n dst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n dst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n dst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n dst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n dst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n dst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n dst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n dst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n dst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n dst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n dst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat4): 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 */\nexport const 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 */\nexport function multiply(a: Mat4, b: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n dst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n dst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n dst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n dst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n dst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n dst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n dst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 3] = a[ 3];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n dst[ 7] = a[ 7];\n dst[ 8] = a[ 8];\n dst[ 9] = a[ 9];\n dst[10] = a[10];\n dst[11] = a[11];\n }\n dst[12] = v[0];\n dst[13] = v[1];\n dst[14] = v[2];\n dst[15] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function setAxis(m: Mat4, v: Vec3, axis: number, dst: Mat4): Mat4 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n dst[off + 2] = v[2];\n return dst;\n}\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 */\nexport function getScaling(m: Mat4, dst?: Vec3): Vec3 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return dst;\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 */\nexport function perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n dst[0] = f / aspect;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = f;\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n dst[10] = zFar * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n } else {\n dst[10] = -1;\n dst[14] = -zNear;\n }\n\n return dst;\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 */export function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: Mat4) {\n dst = dst || new MatType(16);\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n dst[ 0] = f / aspect;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n\n dst[ 4] = 0;\n dst[ 5] = f;\n dst[ 6] = 0;\n dst[ 7] = 0;\n\n dst[ 8] = 0;\n dst[ 9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (zFar === Infinity) {\n dst[10] = 0;\n dst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n dst[10] = zNear * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n }\n\n return dst;\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 */\nexport function ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[0] = 2 / (right - left);\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = 2 / (top - bottom);\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[10] = 1 / (near - far);\n dst[11] = 0;\n\n dst[12] = (right + left) / (left - right);\n dst[13] = (top + bottom) / (bottom - top);\n dst[14] = near / (near - far);\n dst[15] = 1;\n\n return dst;\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 */\nexport function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[10] = far / dz;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = near * far / dz;\n dst[15] = 0;\n\n return dst;\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 */\nexport function frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (far === Infinity) {\n dst[10] = 0;\n dst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n dst[10] = near * rangeInv;\n dst[14] = far * near * rangeInv;\n }\n\n return dst;\n}\n\nlet xAxis: Vec3;\nlet yAxis: Vec3;\nlet zAxis: Vec3;\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 */\nexport function aim(position: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = position[0]; dst[13] = position[1]; dst[14] = position[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function cameraAim(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = eye[0]; dst[13] = eye[1]; dst[14] = eye[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function lookAt(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = yAxis[0]; dst[ 2] = zAxis[0]; dst[ 3] = 0;\n dst[ 4] = xAxis[1]; dst[ 5] = yAxis[1]; dst[ 6] = zAxis[1]; dst[ 7] = 0;\n dst[ 8] = xAxis[2]; dst[ 9] = yAxis[2]; dst[10] = zAxis[2]; dst[11] = 0;\n\n dst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n dst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n dst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n dst[15] = 1;\n\n return dst;\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 */\nexport function translation(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = v[0]; dst[13] = v[1]; dst[14] = v[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 3] = m03;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n dst[ 7] = m13;\n dst[ 8] = m20;\n dst[ 9] = m21;\n dst[10] = m22;\n dst[11] = m23;\n }\n\n dst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n dst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n dst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n dst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return dst;\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 */\nexport function rotationX(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = c; dst[ 6] = s; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = -s; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateX(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[4] = c * m10 + s * m20;\n dst[5] = c * m11 + s * m21;\n dst[6] = c * m12 + s * m22;\n dst[7] = c * m13 + s * m23;\n dst[8] = c * m20 - s * m10;\n dst[9] = c * m21 - s * m11;\n dst[10] = c * m22 - s * m12;\n dst[11] = c * m23 - s * m13;\n\n if (m !== dst) {\n dst[ 0] = m[ 0];\n dst[ 1] = m[ 1];\n dst[ 2] = m[ 2];\n dst[ 3] = m[ 3];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationY(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = 0; dst[ 2] = -s; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = s; dst[ 9] = 0; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateY(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 - s * m20;\n dst[ 1] = c * m01 - s * m21;\n dst[ 2] = c * m02 - s * m22;\n dst[ 3] = c * m03 - s * m23;\n dst[ 8] = c * m20 + s * m00;\n dst[ 9] = c * m21 + s * m01;\n dst[10] = c * m22 + s * m02;\n dst[11] = c * m23 + s * m03;\n\n if (m !== dst) {\n dst[ 4] = m[ 4];\n dst[ 5] = m[ 5];\n dst[ 6] = m[ 6];\n dst[ 7] = m[ 7];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationZ(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateZ(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n dst[ 3] = c * m03 + s * m13;\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n dst[ 7] = c * m13 - s * m03;\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n dst[11] = m[11];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function axisRotation(axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = xx + (1 - xx) * c;\n dst[ 1] = x * y * oneMinusCosine + z * s;\n dst[ 2] = x * z * oneMinusCosine - y * s;\n dst[ 3] = 0;\n dst[ 4] = x * y * oneMinusCosine - z * s;\n dst[ 5] = yy + (1 - yy) * c;\n dst[ 6] = y * z * oneMinusCosine + x * s;\n dst[ 7] = 0;\n dst[ 8] = x * z * oneMinusCosine + y * s;\n dst[ 9] = y * z * oneMinusCosine - x * s;\n dst[10] = zz + (1 - zz) * c;\n dst[11] = 0;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = 0;\n dst[15] = 1;\n\n return dst;\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 */\nexport const 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 */\nexport function axisRotate(m: Mat4, axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n dst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n dst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n dst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n dst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n dst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n dst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n dst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n dst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n dst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n dst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n dst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport const 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 */\nexport function scaling(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = v[2]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n dst[ 3] = v0 * m[0 * 4 + 3];\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n dst[ 7] = v1 * m[1 * 4 + 3];\n dst[ 8] = v2 * m[2 * 4 + 0];\n dst[ 9] = v2 * m[2 * 4 + 1];\n dst[10] = v2 * m[2 * 4 + 2];\n dst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = s; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat4, s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n dst[ 3] = s * m[0 * 4 + 3];\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n dst[ 7] = s * m[1 * 4 + 3];\n dst[ 8] = s * m[2 * 4 + 0];\n dst[ 9] = s * m[2 * 4 + 1];\n dst[10] = s * m[2 * 4 + 2];\n dst[11] = s * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link quat.setDefaultType}.\n */\nexport type Quat = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let QuatType: new (n: number) => Quat = Float32Array;\n\n/**\n * Sets the type this library creates for a Quat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Quat4\n */\nexport function setDefaultType(ctor: new (n: number) => Quat) {\n const oldType = QuatType;\n QuatType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Quat {\n const dst = new QuatType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Quat, create, setDefaultType, QuatType } from './quat';\nimport { Mat3 } from './mat3.js';\nimport { Mat4 } from './mat4.js';\nimport { Vec3 } from './vec3.js';\nimport * as vec3 from './vec3-impl.js';\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\nexport default Quat;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Quat) {\n dst = dst || new QuatType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 **/\nexport function fromAxisAngle(axis: Vec3, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n dst[0] = s * axis[0];\n dst[1] = s * axis[1];\n dst[2] = s * axis[2];\n dst[3] = Math.cos(halfAngle);\n\n return dst;\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 */\nexport function toAxisAngle(q: Quat, dst?: Vec3): { angle: number, axis: Vec3 } {\n dst = dst || vec3.create(4);\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n dst[0] = q[0] / s;\n dst[1] = q[1] / s;\n dst[2] = q[2] / s;\n } else {\n dst[0] = 1;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n return { angle, axis: dst };\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 */\nexport function angle(a: Quat, b: Quat) {\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 */\nexport function multiply(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = ax * bw + aw * bx + ay * bz - az * by;\n dst[1] = ay * bw + aw * by + az * bx - ax * bz;\n dst[2] = az * bw + aw * bz + ax * by - ay * bx;\n dst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return dst;\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 */\nexport const 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 */\nexport function rotateX(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qw * bx;\n dst[1] = qy * bw + qz * bx;\n dst[2] = qz * bw - qy * bx;\n dst[3] = qw * bw - qx * bx;\n\n return dst;\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 */\nexport function rotateY(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw - qz * by;\n dst[1] = qy * bw + qw * by;\n dst[2] = qz * bw + qx * by;\n dst[3] = qw * bw - qy * by;\n\n return dst;\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 */\nexport function rotateZ(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qy * bz;\n dst[1] = qy * bw - qx * bz;\n dst[2] = qz * bw + qw * bz;\n dst[3] = qw * bw - qz * bz;\n\n return dst;\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 */\nexport function slerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = scale0 * ax + scale1 * bx;\n dst[1] = scale0 * ay + scale1 * by;\n dst[2] = scale0 * az + scale1 * bz;\n dst[3] = scale0 * aw + scale1 * bw;\n\n return dst;\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 */\nexport function inverse(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = -a0 * invDot;\n dst[1] = -a1 * invDot;\n dst[2] = -a2 * invDot;\n dst[3] = a3 * invDot;\n\n return dst;\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 */\nexport function conjugate(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = -q[0];\n dst[1] = -q[1];\n dst[2] = -q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport function fromMat(m: Mat3 | Mat4, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n dst[0] = (m[6] - m[9]) * invRoot;\n dst[1] = (m[8] - m[2]) * invRoot;\n dst[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 dst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n dst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n dst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n dst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return dst;\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 */\nexport function fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: Quat) {\n dst = dst || new QuatType(4);\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 dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return dst;\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 */\nexport function copy(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = q[0];\n dst[1] = q[1];\n dst[2] = q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport const 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 */\nexport function add(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function subtract(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function mulScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function dot(a: Quat, b: Quat): 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 */\nexport function lerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nexport function length(v: Quat): 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 */\nexport const 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 */\nexport function lengthSq(v: Quat): 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 */\nexport const 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 */\nexport function normalize(v: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function equalsApproximately(a: Quat, b: Quat): 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 */\nexport function equals(a: Quat, b: Quat): 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 */\nexport function identity(dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n}\n\nlet tempVec3: Vec3;\nlet xUnitVec3: Vec3;\nlet yUnitVec3: Vec3;\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 */\nexport function rotationTo(aUnit: Vec3, bUnit: Vec3, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempVec3 = tempVec3 || vec3.create();\n xUnitVec3 = xUnitVec3 || vec3.create(1, 0, 0);\n yUnitVec3 = yUnitVec3 || vec3.create(0, 1, 0);\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, dst);\n\n return dst;\n } else if (dot > 0.999999) {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n dst[0] = tempVec3[0];\n dst[1] = tempVec3[1];\n dst[2] = tempVec3[2];\n dst[3] = 1 + dot;\n\n return normalize(dst, dst);\n }\n}\n\nlet tempQuat1: Quat;\nlet tempQuat2: Quat;\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 */\nexport function sqlerp(\n a: Quat,\n b: Quat,\n c: Quat,\n d: Quat,\n t: number,\n dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempQuat1 = tempQuat1 || new QuatType(4);\n tempQuat2 = tempQuat2 || new QuatType(4);\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), dst);\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec4.setDefaultType}.\n */\nexport type Vec4 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let VecType: new (n: number) => Vec4 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec4\n */\nexport function setDefaultType(ctor: new (n: number) => Vec4) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Vec4 {\n const dst = new VecType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Vec4, create, setDefaultType, VecType } from './vec4';\nimport { Mat4 } from './mat4';\n\nexport default Vec4;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 */\nexport function ceil(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n dst[3] = Math.ceil(v[3]);\n\n return dst;\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 */\nexport function floor(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n dst[3] = Math.floor(v[3]);\n\n return dst;\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 */\nexport function round(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n dst[3] = Math.round(v[3]);\n\n return dst;\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 */\nexport function clamp(v: Vec4, min = 0, max = 1, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n dst[3] = Math.min(max, Math.max(min, v[3]));\n\n return dst;\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 */\nexport function add(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function addScaled(a: Vec4, b: Vec4, scale: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n dst[3] = a[3] + b[3] * scale;\n\n return dst;\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 */\nexport function subtract(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec4, b: Vec4): 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 */\nexport function equals(a: Vec4, b: Vec4): 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 */\nexport function lerp(a: Vec4, b: Vec4, t: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\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 */\nexport function lerpV(a: Vec4, b: Vec4, t: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n dst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return dst;\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 */\nexport function max(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n dst[3] = Math.max(a[3], b[3]);\n\n return dst;\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 */\nexport function min(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n dst[3] = Math.min(a[3], b[3]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n dst[3] = 1 / v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function dot(a: Vec4, b: Vec4): 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 */\nexport function length(v: Vec4): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec4): 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 */\nexport const 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 */\nexport function distance(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function normalize(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n dst[3] = -v[3];\n\n return dst;\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 */\nexport function copy(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n dst[3] = v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n dst[3] = a[3] * b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n dst[3] = a[3] / b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function zero(dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec4, m: Mat4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n dst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n dst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n dst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n dst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return dst;\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 */\nexport function setLength(a: Vec4, len: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec4, maxLen: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n return lerp(a, b, 0.5, dst);\n}\n","import Mat3, * as mat3 from './mat3-impl';\nimport Mat4, * as mat4 from './mat4-impl';\nimport Quat, * as quat from './quat-impl';\nimport Vec2, * as vec2 from './vec2-impl';\nimport Vec3, * as vec3 from './vec3-impl';\nimport Vec4, * as vec4 from './vec4-impl';\nimport * as utils from './utils';\n\n/**\n * Sets the type this library creates for all types\n *\n * example:\n *\n * ```\n * setDefaultType(Float64Array);\n * ```\n *\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n */\nexport function setDefaultType(ctor: new (n: number) => Float32Array | Float64Array | number[]) {\n mat3.setDefaultType(ctor);\n mat4.setDefaultType(ctor);\n quat.setDefaultType(ctor);\n vec2.setDefaultType(ctor);\n vec3.setDefaultType(ctor);\n vec4.setDefaultType(ctor);\n}\n\nexport {\n Mat3,\n mat3,\n Mat4,\n mat4,\n Quat,\n quat,\n utils,\n Vec2,\n vec2,\n Vec3,\n vec3,\n Vec4,\n 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@@ -/* wgpu-matrix@2.8.3, license MIT */ +/* wgpu-matrix@2.9.0, license MIT */ /* * Copyright 2022 Gregg Tavares * @@ -3339,13 +3339,61 @@ function perspective(fieldOfViewYInRadians, aspect, zNear, zFar, dst) { dst[12] = 0; dst[13] = 0; dst[15] = 0; - if (zFar === Infinity) { + if (Number.isFinite(zFar)) { + const rangeInv = 1 / (zNear - zFar); + dst[10] = zFar * rangeInv; + dst[14] = zFar * zNear * rangeInv; + } + else { dst[10] = -1; dst[14] = -zNear; } + return dst; +} +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height + * of the frustum, the aspect ratio, and the near and far clipping planes. The + * arguments define a frustum extending in the negative z direction. The given + * angle is the vertical angle of the frustum, and the horizontal angle is + * determined to produce the given aspect ratio. The arguments near and far are + * the distances to the near and far clipping planes. Note that near and far + * are not z coordinates, but rather they are distances along the negative + * z-axis. The matrix generated sends the viewing frustum to the unit box. + * We assume a unit box extending from -1 to 1 in the x and y dimensions and + * from 1 (at -zNear) to 0 (at -zFar) in the z dimension. + * + * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians). + * @param aspect - The aspect ratio width / height. + * @param zNear - The depth (negative z coordinate) + * of the near clipping plane. + * @param zFar - The depth (negative z coordinate) + * of the far clipping plane. (default = Infinity) + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The perspective matrix. + */ function perspectiveReverseZ(fieldOfViewYInRadians, aspect, zNear, zFar = Infinity, dst) { + dst = dst || new MatType(16); + const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5); + dst[0] = f / aspect; + dst[1] = 0; + dst[2] = 0; + dst[3] = 0; + dst[4] = 0; + dst[5] = f; + dst[6] = 0; + dst[7] = 0; + dst[8] = 0; + dst[9] = 0; + dst[11] = -1; + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + if (zFar === Infinity) { + dst[10] = 0; + dst[14] = zNear; + } else { - const rangeInv = 1 / (zNear - zFar); - dst[10] = zFar * rangeInv; + const rangeInv = 1 / (zFar - zNear); + dst[10] = zNear * rangeInv; dst[14] = zFar * zNear * rangeInv; } return dst; @@ -3426,6 +3474,53 @@ function frustum(left, right, bottom, top, near, far, dst) { dst[15] = 0; return dst; } +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right, + * top, bottom, near and far clipping planes. The arguments define a frustum + * extending in the negative z direction. The arguments near and far are the + * distances to the near and far clipping planes. Note that near and far are not + * z coordinates, but rather they are distances along the negative z-axis. The + * matrix generated sends the viewing frustum to the unit box. We assume a unit + * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z + * dimension. + * @param left - The x coordinate of the left plane of the box. + * @param right - The x coordinate of the right plane of the box. + * @param bottom - The y coordinate of the bottom plane of the box. + * @param top - The y coordinate of the right plane of the box. + * @param near - The negative z coordinate of the near plane of the box. + * @param far - The negative z coordinate of the far plane of the box. + * @param dst - Output matrix. If not passed a new one is created. + * @returns The perspective projection matrix. + */ +function frustumReverseZ(left, right, bottom, top, near, far = Infinity, dst) { + dst = dst || new MatType(16); + const dx = (right - left); + const dy = (top - bottom); + dst[0] = 2 * near / dx; + dst[1] = 0; + dst[2] = 0; + dst[3] = 0; + dst[4] = 0; + dst[5] = 2 * near / dy; + dst[6] = 0; + dst[7] = 0; + dst[8] = (left + right) / dx; + dst[9] = (top + bottom) / dy; + dst[11] = -1; + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + if (far === Infinity) { + dst[10] = 0; + dst[14] = near; + } + else { + const rangeInv = 1 / (far - near); + dst[10] = near * rangeInv; + dst[14] = far * near * rangeInv; + } + return dst; +} let xAxis; let yAxis; let zAxis; @@ -4093,6 +4188,7 @@ var mat4Impl = { fromMat3: fromMat3, fromQuat: fromQuat, frustum: frustum, + frustumReverseZ: frustumReverseZ, getAxis: getAxis, getScaling: getScaling, getTranslation: getTranslation, @@ -4105,6 +4201,7 @@ var mat4Impl = { negate: negate$1, ortho: ortho, perspective: perspective, + perspectiveReverseZ: perspectiveReverseZ, rotate: rotate, rotateX: rotateX$1, rotateY: rotateY$1, diff --git a/dist/2.x/wgpu-matrix.module.js.map b/dist/2.x/wgpu-matrix.module.js.map index 84a3dee..ead4068 100644 --- a/dist/2.x/wgpu-matrix.module.js.map +++ b/dist/2.x/wgpu-matrix.module.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/utils.ts","../../../src/vec2.ts","../../../src/vec3.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat.ts","../../../src/quat-impl.ts","../../../src/vec4.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/*\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 */\n\n/**\n * A JavaScript array with 2 values, Float32Array with 2 values, or a Float64Array with 2 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec2.setDefaultType}.\n */\nexport type Vec2 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec2 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new Vec2. In other words you can do this\n *\n * const v = vec2.cross(v1, v2); // Creates a new Vec2 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec2.create();\n * vec2.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 * vec2.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec2 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec2\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec2\n */\nexport function setDefaultType(ctor: new (n: number) => Vec2) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Vec2Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `vec2.create` is usually used\n * to create a Vec2 to be filled out as in\n *\n * ```\n * const sum = vec2.create();\n * vec2.add(v1, v2, sum);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nexport function create(x = 0, y = 0): Vec2 {\n const dst = new VecType(2);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n }\n }\n return dst;\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\n/**\n * A JavaScript array with 3 values, Float32Array with 3 values, or a Float64Array with 3 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec3.setDefaultType}.\n */\nexport type Vec3 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec3 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new `Vec3`. In other words you can do this\n *\n * const v = vec3.cross(v1, v2); // Creates a new Vec3 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec3.create();\n * vec3.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 * vec3.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec3 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec3\n */\nexport function setDefaultType(ctor: new (n: number) => Vec3) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number): Vec3 {\n const dst = new VecType(3);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n }\n }\n }\n return dst;\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 { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Vec2, create, setDefaultType, VecType } from './vec2';\nimport { Vec3, VecType as Vec3Type } from './vec3';\n\nexport default Vec2;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = x;\n dst[1] = y;\n\n return dst;\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 */\nexport function ceil(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n\n return dst;\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 */\nexport function floor(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n\n return dst;\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 */\nexport function round(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n\n return dst;\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 */\nexport function clamp(v: Vec2, min = 0, max = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n\n return dst;\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 */\nexport function add(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n\n return dst;\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 */\nexport function addScaled(a: Vec2, b: Vec2, scale: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec2, b: Vec2): 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 */\nexport function subtract(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec2, b: Vec2): 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 */\nexport function equals(a: Vec2, b: Vec2): 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 */\nexport function lerp(a: Vec2, b: Vec2, t: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n\n return dst;\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 */\nexport function lerpV(a: Vec2, b: Vec2, t: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return dst;\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 */\nexport function max(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n\n return dst;\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 */\nexport function min(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec2, b: Vec2, dst?: Vec3): Vec3 {\n dst = dst || new Vec3Type(3);\n const z = a[0] * b[1] - a[1] * b[0];\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = z;\n\n return dst;\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 */\nexport function dot(a: Vec2, b: Vec2): 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 */\nexport function length(v: Vec2): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec2): 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 */\nexport const 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 */\nexport function distance(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function normalize(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n\n return dst;\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 */\nexport function copy(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0];\n dst[1] = v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const angle = Math.random() * 2 * Math.PI;\n dst[0] = Math.cos(angle) * scale;\n dst[1] = Math.sin(angle) * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 0;\n dst[1] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec2, m: Mat4, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = x * m[0] + y * m[4] + m[12];\n dst[1] = x * m[1] + y * m[5] + m[13];\n\n return dst;\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 */\nexport function transformMat3(v: Vec2, m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = m[0] * x + m[4] * y + m[8];\n dst[1] = m[1] * x + m[5] * y + m[9];\n\n return dst;\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 */\nexport function rotate(a: Vec2, b: Vec2, rad: number, dst?: Vec2) {\n dst = dst || new VecType(2);\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 dst[0] = p0 * cosC - p1 * sinC + b[0];\n dst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return dst;\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 */\nexport function setLength(a: Vec2, len: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec2, maxLen: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n return lerp(a, b, 0.5, dst);\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 { Quat } from './quat';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport Vec2, * as vec2 from './vec2-impl';\n\nexport default Mat3;\n\nexport type Mat3LikeCtor = new (n: number) => Mat3;\n\n/**\n * 3x3 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 = mat3.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat3.create();\n * mat3.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 = mat3.identity();\n * const trans = mat3.translation([1, 2, 3]);\n * mat3.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\nlet MatType: Mat3LikeCtor = Float32Array;\n\n// This mess is because with Mat3 we have 3 unused elements.\n// For Float32Array and Float64Array that's not an issue\n// but for Array it's troublesome\nconst ctorMap = new Map Mat3>([\n [Float32Array, () => new Float32Array(12)],\n [Float64Array, () => new Float64Array(12)],\n [Array, () => new Array(12).fill(0)],\n]);\nlet newMat3: () => Mat3 = ctorMap.get(Float32Array)!;\n\n/**\n * Sets the type this library creates for a Mat3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat3\n */\nexport function setDefaultType(ctor: new (n: number) => Mat3) {\n const oldType = MatType;\n MatType = ctor;\n newMat3 = ctorMap.get(ctor)!;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Mat3Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat3.create` is usually used\n * to create a Mat3 to be filled out as in\n *\n * ```\n * const m = mat3.create();\n * mat3.perspective(fov, aspect, near, far, m);\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 */\nexport function create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number): Mat3 {\n const dst = newMat3();\n // to make the array homogenous\n dst[3] = 0;\n dst[7] = 0;\n dst[11] = 0;\n\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[4] = v3;\n if (v4 !== undefined) {\n dst[5] = v4;\n if (v5 !== undefined) {\n dst[6] = v5;\n if (v6 !== undefined) {\n dst[8] = v6;\n if (v7 !== undefined) {\n dst[9] = v7;\n if (v8 !== undefined) {\n dst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return dst;\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 */\nexport function set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: Mat3) {\n dst = dst || newMat3();\n\n dst[0] = v0; dst[1] = v1; dst[ 2] = v2; dst[ 3] = 0;\n dst[4] = v3; dst[5] = v4; dst[ 6] = v5; dst[ 7] = 0;\n dst[8] = v6; dst[9] = v7; dst[10] = v8; dst[11] = 0;\n\n return dst;\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 */\nexport function fromMat4(m4: Mat4, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n dst[0] = m4[0]; dst[1] = m4[1]; dst[ 2] = m4[ 2]; dst[ 3] = 0;\n dst[4] = m4[4]; dst[5] = m4[5]; dst[ 6] = m4[ 6]; dst[ 7] = 0;\n dst[8] = m4[8]; dst[9] = m4[9]; dst[10] = m4[10]; dst[11] = 0;\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n\n return dst;\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 */\nexport function negate(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10];\n\n return dst;\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 */\nexport function copy(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat3, b: Mat3): 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 */\nexport function equals(a: Mat3, b: Mat3): 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 */\nexport function identity(dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22;\n\n return dst;\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 */\nexport function inverse(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = b01 * invDet;\n dst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n dst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n dst[ 4] = b11 * invDet;\n dst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n dst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n dst[ 8] = b21 * invDet;\n dst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n dst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat3): 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 */\nexport const 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 */\nexport function multiply(a: Mat3, b: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n }\n dst[ 8] = v[0];\n dst[ 9] = v[1];\n dst[10] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n dst[0] = m[8];\n dst[1] = m[9];\n return dst;\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 */\nexport function getAxis(m: Mat3, axis: number, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n return dst;\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 */\nexport function setAxis(m: Mat3, v: Vec2, axis: number, dst?: Mat3): Mat3 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n return dst;\n}\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 */\nexport function getScaling(m: Mat3, dst?: Vec2): Vec2 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy);\n dst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return dst;\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 */\nexport function translation(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = v[0]; dst[ 9] = v[1]; dst[10] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n }\n\n dst[ 8] = m00 * v0 + m10 * v1 + m20;\n dst[ 9] = m01 * v0 + m11 * v1 + m21;\n dst[10] = m02 * v0 + m12 * v1 + m22;\n\n return dst;\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 */\nexport function rotation(angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function rotate(m: Mat3, angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function scaling(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const v0 = v[0];\n const v1 = v[1];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat3, s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 { Vec3, create, setDefaultType, VecType } from './vec3';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\n\nexport default Vec3;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n\n return dst;\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 */\nexport function ceil(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n\n return dst;\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 */\nexport function floor(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n\n return dst;\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 */\nexport function round(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n\n return dst;\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 */\nexport function clamp(v: Vec3, min = 0, max = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n\n return dst;\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 */\nexport function add(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n\n return dst;\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 */\nexport function addScaled(a: Vec3, b: Vec3, scale: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec3, b: Vec3): 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 */\nexport function subtract(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec3, b: Vec3): 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 */\nexport function equals(a: Vec3, b: Vec3): 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 */\nexport function lerp(a: Vec3, b: Vec3, t: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n\n return dst;\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 */\nexport function lerpV(a: Vec3, b: Vec3, t: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return dst;\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 */\nexport function max(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n\n return dst;\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 */\nexport function min(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n dst[0] = a[1] * b[2] - a[2] * b[1];\n dst[1] = t1;\n dst[2] = t2;\n\n return dst;\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 */\nexport function dot(a: Vec3, b: Vec3): 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 */\nexport function length(v: Vec3): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec3): 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 */\nexport const 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 */\nexport function distance(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function normalize(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n\n return dst;\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 */\nexport function negate(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n\n return dst;\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 */\nexport function copy(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = Math.cos(angle) * zScale;\n dst[1] = Math.sin(angle) * zScale;\n dst[2] = z * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n dst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n dst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return dst;\n}\n\n/**\n * Transform vec4 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 */\nexport function transformMat4Upper3x3(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return dst;\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 */\nexport function transformMat3(v: Vec3, m: Mat3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n dst[0] = x * m[0] + y * m[4] + z * m[8];\n dst[1] = x * m[1] + y * m[5] + z * m[9];\n dst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return dst;\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 */\nexport function transformQuat(v: Vec3, q: Quat, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n dst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n dst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec3) {\n dst = dst || new VecType(3);\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function getScaling(m: Mat4, dst: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return dst;\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 */\nexport function rotateX(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateY(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateZ(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function setLength(a: Vec3, len: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec3, maxLen: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n return lerp(a, b, 0.5, dst);\n}\n","\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\nimport Vec3, * as vec3 from './vec3-impl';\nimport * as utils from './utils';\n\nexport default Mat4;\n\nexport type Mat4LikeCtor = new (n: number) => Mat4;\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 */\nlet MatType: Mat4LikeCtor = Float32Array;\n\n/**\n * Sets the type this library creates for a Mat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat4\n */\nexport function setDefaultType(ctor: new (n: number) => Mat4) {\n const oldType = MatType;\n MatType = ctor;\n return oldType;\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 * Note: a consequence of the implementation is if your Mat4Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat4.create` is usually used\n * to create a Mat4 to be filled out as in\n *\n * ```\n * const m = mat4.create();\n * mat4.perspective(fov, aspect, near, far, m);\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 */\nexport function 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): Mat4 {\n const dst = new MatType(16);\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[3] = v3;\n if (v4 !== undefined) {\n dst[4] = v4;\n if (v5 !== undefined) {\n dst[5] = v5;\n if (v6 !== undefined) {\n dst[6] = v6;\n if (v7 !== undefined) {\n dst[7] = v7;\n if (v8 !== undefined) {\n dst[8] = v8;\n if (v9 !== undefined) {\n dst[9] = v9;\n if (v10 !== undefined) {\n dst[10] = v10;\n if (v11 !== undefined) {\n dst[11] = v11;\n if (v12 !== undefined) {\n dst[12] = v12;\n if (v13 !== undefined) {\n dst[13] = v13;\n if (v14 !== undefined) {\n dst[14] = v14;\n if (v15 !== undefined) {\n dst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return dst;\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 */\nexport function 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?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v0; dst[ 1] = v1; dst[ 2] = v2; dst[ 3] = v3;\n dst[ 4] = v4; dst[ 5] = v5; dst[ 6] = v6; dst[ 7] = v7;\n dst[ 8] = v8; dst[ 9] = v9; dst[10] = v10; dst[11] = v11;\n dst[12] = v12; dst[13] = v13; dst[14] = v14; dst[15] = v15;\n\n return dst;\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 */\nexport function fromMat3(m3: Mat3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m3[0]; dst[ 1] = m3[1]; dst[ 2] = m3[ 2]; dst[ 3] = 0;\n dst[ 4] = m3[4]; dst[ 5] = m3[5]; dst[ 6] = m3[ 6]; dst[ 7] = 0;\n dst[ 8] = m3[8]; dst[ 9] = m3[9]; dst[10] = m3[10]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function negate(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2]; dst[ 3] = -m[ 3];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6]; dst[ 7] = -m[ 7];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10]; dst[11] = -m[11];\n dst[12] = -m[12]; dst[13] = -m[13]; dst[14] = -m[14]; dst[15] = -m[15];\n\n return dst;\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 */\nexport function copy(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2]; dst[ 3] = m[ 3];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6]; dst[ 7] = m[ 7];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10]; dst[11] = m[11];\n dst[12] = m[12]; dst[13] = m[13]; dst[14] = m[14]; dst[15] = m[15];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat4, b: Mat4): 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 */\nexport function equals(a: Mat4, b: Mat4): 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 */\nexport function identity(dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20; dst[ 3] = m30;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21; dst[ 7] = m31;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22; dst[11] = m32;\n dst[12] = m03; dst[13] = m13; dst[14] = m23; dst[15] = m33;\n\n return dst;\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 */\nexport function inverse(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = d * t0;\n dst[ 1] = d * t1;\n dst[ 2] = d * t2;\n dst[ 3] = d * t3;\n dst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n dst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n dst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n dst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n dst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n dst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n dst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n dst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n dst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n dst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n dst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n dst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat4): 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 */\nexport const 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 */\nexport function multiply(a: Mat4, b: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n dst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n dst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n dst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n dst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n dst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n dst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n dst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 3] = a[ 3];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n dst[ 7] = a[ 7];\n dst[ 8] = a[ 8];\n dst[ 9] = a[ 9];\n dst[10] = a[10];\n dst[11] = a[11];\n }\n dst[12] = v[0];\n dst[13] = v[1];\n dst[14] = v[2];\n dst[15] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function setAxis(m: Mat4, v: Vec3, axis: number, dst: Mat4): Mat4 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n dst[off + 2] = v[2];\n return dst;\n}\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 */\nexport function getScaling(m: Mat4, dst?: Vec3): Vec3 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return dst;\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 */\nexport function perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n dst[0] = f / aspect;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = f;\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (zFar === Infinity) {\n dst[10] = -1;\n dst[14] = -zNear;\n } else {\n const rangeInv = 1 / (zNear - zFar);\n dst[10] = zFar * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n }\n\n return dst;\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 */\nexport function ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[0] = 2 / (right - left);\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = 2 / (top - bottom);\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[10] = 1 / (near - far);\n dst[11] = 0;\n\n dst[12] = (right + left) / (left - right);\n dst[13] = (top + bottom) / (bottom - top);\n dst[14] = near / (near - far);\n dst[15] = 1;\n\n return dst;\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 */\nexport function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[10] = far / dz;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = near * far / dz;\n dst[15] = 0;\n\n return dst;\n}\n\nlet xAxis: Vec3;\nlet yAxis: Vec3;\nlet zAxis: Vec3;\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 */\nexport function aim(position: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = position[0]; dst[13] = position[1]; dst[14] = position[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function cameraAim(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = eye[0]; dst[13] = eye[1]; dst[14] = eye[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function lookAt(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = yAxis[0]; dst[ 2] = zAxis[0]; dst[ 3] = 0;\n dst[ 4] = xAxis[1]; dst[ 5] = yAxis[1]; dst[ 6] = zAxis[1]; dst[ 7] = 0;\n dst[ 8] = xAxis[2]; dst[ 9] = yAxis[2]; dst[10] = zAxis[2]; dst[11] = 0;\n\n dst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n dst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n dst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n dst[15] = 1;\n\n return dst;\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 */\nexport function translation(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = v[0]; dst[13] = v[1]; dst[14] = v[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 3] = m03;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n dst[ 7] = m13;\n dst[ 8] = m20;\n dst[ 9] = m21;\n dst[10] = m22;\n dst[11] = m23;\n }\n\n dst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n dst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n dst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n dst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return dst;\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 */\nexport function rotationX(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = c; dst[ 6] = s; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = -s; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateX(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[4] = c * m10 + s * m20;\n dst[5] = c * m11 + s * m21;\n dst[6] = c * m12 + s * m22;\n dst[7] = c * m13 + s * m23;\n dst[8] = c * m20 - s * m10;\n dst[9] = c * m21 - s * m11;\n dst[10] = c * m22 - s * m12;\n dst[11] = c * m23 - s * m13;\n\n if (m !== dst) {\n dst[ 0] = m[ 0];\n dst[ 1] = m[ 1];\n dst[ 2] = m[ 2];\n dst[ 3] = m[ 3];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationY(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = 0; dst[ 2] = -s; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = s; dst[ 9] = 0; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateY(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 - s * m20;\n dst[ 1] = c * m01 - s * m21;\n dst[ 2] = c * m02 - s * m22;\n dst[ 3] = c * m03 - s * m23;\n dst[ 8] = c * m20 + s * m00;\n dst[ 9] = c * m21 + s * m01;\n dst[10] = c * m22 + s * m02;\n dst[11] = c * m23 + s * m03;\n\n if (m !== dst) {\n dst[ 4] = m[ 4];\n dst[ 5] = m[ 5];\n dst[ 6] = m[ 6];\n dst[ 7] = m[ 7];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationZ(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateZ(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n dst[ 3] = c * m03 + s * m13;\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n dst[ 7] = c * m13 - s * m03;\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n dst[11] = m[11];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function axisRotation(axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = xx + (1 - xx) * c;\n dst[ 1] = x * y * oneMinusCosine + z * s;\n dst[ 2] = x * z * oneMinusCosine - y * s;\n dst[ 3] = 0;\n dst[ 4] = x * y * oneMinusCosine - z * s;\n dst[ 5] = yy + (1 - yy) * c;\n dst[ 6] = y * z * oneMinusCosine + x * s;\n dst[ 7] = 0;\n dst[ 8] = x * z * oneMinusCosine + y * s;\n dst[ 9] = y * z * oneMinusCosine - x * s;\n dst[10] = zz + (1 - zz) * c;\n dst[11] = 0;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = 0;\n dst[15] = 1;\n\n return dst;\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 */\nexport const 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 */\nexport function axisRotate(m: Mat4, axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n dst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n dst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n dst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n dst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n dst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n dst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n dst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n dst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n dst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n dst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n dst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport const 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 */\nexport function scaling(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = v[2]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n dst[ 3] = v0 * m[0 * 4 + 3];\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n dst[ 7] = v1 * m[1 * 4 + 3];\n dst[ 8] = v2 * m[2 * 4 + 0];\n dst[ 9] = v2 * m[2 * 4 + 1];\n dst[10] = v2 * m[2 * 4 + 2];\n dst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = s; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat4, s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n dst[ 3] = s * m[0 * 4 + 3];\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n dst[ 7] = s * m[1 * 4 + 3];\n dst[ 8] = s * m[2 * 4 + 0];\n dst[ 9] = s * m[2 * 4 + 1];\n dst[10] = s * m[2 * 4 + 2];\n dst[11] = s * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link quat.setDefaultType}.\n */\nexport type Quat = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let QuatType: new (n: number) => Quat = Float32Array;\n\n/**\n * Sets the type this library creates for a Quat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Quat4\n */\nexport function setDefaultType(ctor: new (n: number) => Quat) {\n const oldType = QuatType;\n QuatType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Quat {\n const dst = new QuatType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Quat, create, setDefaultType, QuatType } from './quat';\nimport { Mat3 } from './mat3.js';\nimport { Mat4 } from './mat4.js';\nimport { Vec3 } from './vec3.js';\nimport * as vec3 from './vec3-impl.js';\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\nexport default Quat;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Quat) {\n dst = dst || new QuatType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 **/\nexport function fromAxisAngle(axis: Vec3, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n dst[0] = s * axis[0];\n dst[1] = s * axis[1];\n dst[2] = s * axis[2];\n dst[3] = Math.cos(halfAngle);\n\n return dst;\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 */\nexport function toAxisAngle(q: Quat, dst?: Vec3): { angle: number, axis: Vec3 } {\n dst = dst || vec3.create(4);\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n dst[0] = q[0] / s;\n dst[1] = q[1] / s;\n dst[2] = q[2] / s;\n } else {\n dst[0] = 1;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n return { angle, axis: dst };\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 */\nexport function angle(a: Quat, b: Quat) {\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 */\nexport function multiply(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = ax * bw + aw * bx + ay * bz - az * by;\n dst[1] = ay * bw + aw * by + az * bx - ax * bz;\n dst[2] = az * bw + aw * bz + ax * by - ay * bx;\n dst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return dst;\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 */\nexport const 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 */\nexport function rotateX(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qw * bx;\n dst[1] = qy * bw + qz * bx;\n dst[2] = qz * bw - qy * bx;\n dst[3] = qw * bw - qx * bx;\n\n return dst;\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 */\nexport function rotateY(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw - qz * by;\n dst[1] = qy * bw + qw * by;\n dst[2] = qz * bw + qx * by;\n dst[3] = qw * bw - qy * by;\n\n return dst;\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 */\nexport function rotateZ(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qy * bz;\n dst[1] = qy * bw - qx * bz;\n dst[2] = qz * bw + qw * bz;\n dst[3] = qw * bw - qz * bz;\n\n return dst;\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 */\nexport function slerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = scale0 * ax + scale1 * bx;\n dst[1] = scale0 * ay + scale1 * by;\n dst[2] = scale0 * az + scale1 * bz;\n dst[3] = scale0 * aw + scale1 * bw;\n\n return dst;\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 */\nexport function inverse(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = -a0 * invDot;\n dst[1] = -a1 * invDot;\n dst[2] = -a2 * invDot;\n dst[3] = a3 * invDot;\n\n return dst;\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 */\nexport function conjugate(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = -q[0];\n dst[1] = -q[1];\n dst[2] = -q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport function fromMat(m: Mat3 | Mat4, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n dst[0] = (m[6] - m[9]) * invRoot;\n dst[1] = (m[8] - m[2]) * invRoot;\n dst[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 dst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n dst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n dst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n dst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return dst;\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 */\nexport function fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: Quat) {\n dst = dst || new QuatType(4);\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 dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return dst;\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 */\nexport function copy(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = q[0];\n dst[1] = q[1];\n dst[2] = q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport const 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 */\nexport function add(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function subtract(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function mulScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function dot(a: Quat, b: Quat): 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 */\nexport function lerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nexport function length(v: Quat): 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 */\nexport const 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 */\nexport function lengthSq(v: Quat): 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 */\nexport const 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 */\nexport function normalize(v: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function equalsApproximately(a: Quat, b: Quat): 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 */\nexport function equals(a: Quat, b: Quat): 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 */\nexport function identity(dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n}\n\nlet tempVec3: Vec3;\nlet xUnitVec3: Vec3;\nlet yUnitVec3: Vec3;\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 */\nexport function rotationTo(aUnit: Vec3, bUnit: Vec3, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempVec3 = tempVec3 || vec3.create();\n xUnitVec3 = xUnitVec3 || vec3.create(1, 0, 0);\n yUnitVec3 = yUnitVec3 || vec3.create(0, 1, 0);\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, dst);\n\n return dst;\n } else if (dot > 0.999999) {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n dst[0] = tempVec3[0];\n dst[1] = tempVec3[1];\n dst[2] = tempVec3[2];\n dst[3] = 1 + dot;\n\n return normalize(dst, dst);\n }\n}\n\nlet tempQuat1: Quat;\nlet tempQuat2: Quat;\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 */\nexport function sqlerp(\n a: Quat,\n b: Quat,\n c: Quat,\n d: Quat,\n t: number,\n dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempQuat1 = tempQuat1 || new QuatType(4);\n tempQuat2 = tempQuat2 || new QuatType(4);\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), dst);\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec4.setDefaultType}.\n */\nexport type Vec4 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let VecType: new (n: number) => Vec4 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec4\n */\nexport function setDefaultType(ctor: new (n: number) => Vec4) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Vec4 {\n const dst = new VecType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Vec4, create, setDefaultType, VecType } from './vec4';\nimport { Mat4 } from './mat4';\n\nexport default Vec4;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 */\nexport function ceil(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n dst[3] = Math.ceil(v[3]);\n\n return dst;\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 */\nexport function floor(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n dst[3] = Math.floor(v[3]);\n\n return dst;\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 */\nexport function round(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n dst[3] = Math.round(v[3]);\n\n return dst;\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 */\nexport function clamp(v: Vec4, min = 0, max = 1, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n dst[3] = Math.min(max, Math.max(min, v[3]));\n\n return dst;\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 */\nexport function add(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function addScaled(a: Vec4, b: Vec4, scale: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n dst[3] = a[3] + b[3] * scale;\n\n return dst;\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 */\nexport function subtract(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec4, b: Vec4): 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 */\nexport function equals(a: Vec4, b: Vec4): 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 */\nexport function lerp(a: Vec4, b: Vec4, t: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\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 */\nexport function lerpV(a: Vec4, b: Vec4, t: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n dst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return dst;\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 */\nexport function max(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n dst[3] = Math.max(a[3], b[3]);\n\n return dst;\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 */\nexport function min(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n dst[3] = Math.min(a[3], b[3]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n dst[3] = 1 / v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function dot(a: Vec4, b: Vec4): 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 */\nexport function length(v: Vec4): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec4): 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 */\nexport const 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 */\nexport function distance(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function normalize(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n dst[3] = -v[3];\n\n return dst;\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 */\nexport function copy(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n dst[3] = v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n dst[3] = a[3] * b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n dst[3] = a[3] / b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function zero(dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec4, m: Mat4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n dst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n dst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n dst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n dst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return dst;\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 */\nexport function setLength(a: Vec4, len: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec4, maxLen: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n return lerp(a, b, 0.5, dst);\n}\n","import Mat3, * as mat3 from './mat3-impl';\nimport Mat4, * as mat4 from './mat4-impl';\nimport Quat, * as quat from './quat-impl';\nimport Vec2, * as vec2 from './vec2-impl';\nimport Vec3, * as vec3 from './vec3-impl';\nimport Vec4, * as vec4 from './vec4-impl';\nimport * as utils from './utils';\n\n/**\n * Sets the type this library creates for all types\n *\n * example:\n *\n * ```\n * setDefaultType(Float64Array);\n * ```\n *\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n */\nexport function setDefaultType(ctor: new (n: number) => Float32Array | Float64Array | number[]) {\n mat3.setDefaultType(ctor);\n mat4.setDefaultType(ctor);\n quat.setDefaultType(ctor);\n vec2.setDefaultType(ctor);\n vec3.setDefaultType(ctor);\n vec4.setDefaultType(ctor);\n}\n\nexport {\n Mat3,\n mat3,\n Mat4,\n mat4,\n Quat,\n quat,\n utils,\n Vec2,\n vec2,\n Vec3,\n vec3,\n Vec4,\n 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/utils.ts","../../../src/vec2.ts","../../../src/vec3.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat.ts","../../../src/quat-impl.ts","../../../src/vec4.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/*\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 */\n\n/**\n * A JavaScript array with 2 values, Float32Array with 2 values, or a Float64Array with 2 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec2.setDefaultType}.\n */\nexport type Vec2 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec2 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new Vec2. In other words you can do this\n *\n * const v = vec2.cross(v1, v2); // Creates a new Vec2 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec2.create();\n * vec2.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 * vec2.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec2 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec2\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec2\n */\nexport function setDefaultType(ctor: new (n: number) => Vec2) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Vec2Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `vec2.create` is usually used\n * to create a Vec2 to be filled out as in\n *\n * ```\n * const sum = vec2.create();\n * vec2.add(v1, v2, sum);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nexport function create(x = 0, y = 0): Vec2 {\n const dst = new VecType(2);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n }\n }\n return dst;\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\n/**\n * A JavaScript array with 3 values, Float32Array with 3 values, or a Float64Array with 3 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec3.setDefaultType}.\n */\nexport type Vec3 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec3 math functions.\n *\n * Almost all functions take an optional `dst` argument. If it is not passed in the\n * functions will create a new `Vec3`. In other words you can do this\n *\n * const v = vec3.cross(v1, v2); // Creates a new Vec3 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec3.create();\n * vec3.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 * vec3.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\n\nexport let VecType: new (n: number) => Vec3 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec3\n */\nexport function setDefaultType(ctor: new (n: number) => Vec3) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number): Vec3 {\n const dst = new VecType(3);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n }\n }\n }\n return dst;\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 { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Vec2, create, setDefaultType, VecType } from './vec2';\nimport { Vec3, VecType as Vec3Type } from './vec3';\n\nexport default Vec2;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = x;\n dst[1] = y;\n\n return dst;\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 */\nexport function ceil(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n\n return dst;\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 */\nexport function floor(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n\n return dst;\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 */\nexport function round(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n\n return dst;\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 */\nexport function clamp(v: Vec2, min = 0, max = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n\n return dst;\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 */\nexport function add(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n\n return dst;\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 */\nexport function addScaled(a: Vec2, b: Vec2, scale: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec2, b: Vec2): 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 */\nexport function subtract(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec2, b: Vec2): 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 */\nexport function equals(a: Vec2, b: Vec2): 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 */\nexport function lerp(a: Vec2, b: Vec2, t: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n\n return dst;\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 */\nexport function lerpV(a: Vec2, b: Vec2, t: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return dst;\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 */\nexport function max(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n\n return dst;\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 */\nexport function min(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec2, k: number, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec2, b: Vec2, dst?: Vec3): Vec3 {\n dst = dst || new Vec3Type(3);\n const z = a[0] * b[1] - a[1] * b[0];\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = z;\n\n return dst;\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 */\nexport function dot(a: Vec2, b: Vec2): 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 */\nexport function length(v: Vec2): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec2): 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 */\nexport const 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 */\nexport function distance(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec2, b: Vec2): 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 */\nexport const 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 */\nexport function normalize(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n\n return dst;\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 */\nexport function copy(v: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = v[0];\n dst[1] = v[1];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec2, b: Vec2, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const angle = Math.random() * 2 * Math.PI;\n dst[0] = Math.cos(angle) * scale;\n dst[1] = Math.sin(angle) * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n dst[0] = 0;\n dst[1] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec2, m: Mat4, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = x * m[0] + y * m[4] + m[12];\n dst[1] = x * m[1] + y * m[5] + m[13];\n\n return dst;\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 */\nexport function transformMat3(v: Vec2, m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || new VecType(2);\n\n const x = v[0];\n const y = v[1];\n\n dst[0] = m[0] * x + m[4] * y + m[8];\n dst[1] = m[1] * x + m[5] * y + m[9];\n\n return dst;\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 */\nexport function rotate(a: Vec2, b: Vec2, rad: number, dst?: Vec2) {\n dst = dst || new VecType(2);\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 dst[0] = p0 * cosC - p1 * sinC + b[0];\n dst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return dst;\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 */\nexport function setLength(a: Vec2, len: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec2, maxLen: number, dst?: Vec2) {\n dst = dst || new VecType(2);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec2, b: Vec2, dst?: Vec2) {\n dst = dst || new VecType(2);\n return lerp(a, b, 0.5, dst);\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 { Quat } from './quat';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport Vec2, * as vec2 from './vec2-impl';\n\nexport default Mat3;\n\nexport type Mat3LikeCtor = new (n: number) => Mat3;\n\n/**\n * 3x3 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 = mat3.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat3.create();\n * mat3.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 = mat3.identity();\n * const trans = mat3.translation([1, 2, 3]);\n * mat3.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\nlet MatType: Mat3LikeCtor = Float32Array;\n\n// This mess is because with Mat3 we have 3 unused elements.\n// For Float32Array and Float64Array that's not an issue\n// but for Array it's troublesome\nconst ctorMap = new Map Mat3>([\n [Float32Array, () => new Float32Array(12)],\n [Float64Array, () => new Float64Array(12)],\n [Array, () => new Array(12).fill(0)],\n]);\nlet newMat3: () => Mat3 = ctorMap.get(Float32Array)!;\n\n/**\n * Sets the type this library creates for a Mat3\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat3\n */\nexport function setDefaultType(ctor: new (n: number) => Mat3) {\n const oldType = MatType;\n MatType = ctor;\n newMat3 = ctorMap.get(ctor)!;\n return oldType;\n}\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 * Note: a consequence of the implementation is if your Mat3Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat3.create` is usually used\n * to create a Mat3 to be filled out as in\n *\n * ```\n * const m = mat3.create();\n * mat3.perspective(fov, aspect, near, far, m);\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 */\nexport function create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number): Mat3 {\n const dst = newMat3();\n // to make the array homogenous\n dst[3] = 0;\n dst[7] = 0;\n dst[11] = 0;\n\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[4] = v3;\n if (v4 !== undefined) {\n dst[5] = v4;\n if (v5 !== undefined) {\n dst[6] = v5;\n if (v6 !== undefined) {\n dst[8] = v6;\n if (v7 !== undefined) {\n dst[9] = v7;\n if (v8 !== undefined) {\n dst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return dst;\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 */\nexport function set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: Mat3) {\n dst = dst || newMat3();\n\n dst[0] = v0; dst[1] = v1; dst[ 2] = v2; dst[ 3] = 0;\n dst[4] = v3; dst[5] = v4; dst[ 6] = v5; dst[ 7] = 0;\n dst[8] = v6; dst[9] = v7; dst[10] = v8; dst[11] = 0;\n\n return dst;\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 */\nexport function fromMat4(m4: Mat4, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n dst[0] = m4[0]; dst[1] = m4[1]; dst[ 2] = m4[ 2]; dst[ 3] = 0;\n dst[4] = m4[4]; dst[5] = m4[5]; dst[ 6] = m4[ 6]; dst[ 7] = 0;\n dst[8] = m4[8]; dst[9] = m4[9]; dst[10] = m4[10]; dst[11] = 0;\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n\n return dst;\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 */\nexport function negate(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10];\n\n return dst;\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 */\nexport function copy(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat3, b: Mat3): 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 */\nexport function equals(a: Mat3, b: Mat3): 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 */\nexport function identity(dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22;\n\n return dst;\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 */\nexport function inverse(m: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = b01 * invDet;\n dst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n dst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n dst[ 4] = b11 * invDet;\n dst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n dst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n dst[ 8] = b21 * invDet;\n dst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n dst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat3): 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 */\nexport const 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 */\nexport function multiply(a: Mat3, b: Mat3, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n }\n dst[ 8] = v[0];\n dst[ 9] = v[1];\n dst[10] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n dst[0] = m[8];\n dst[1] = m[9];\n return dst;\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 */\nexport function getAxis(m: Mat3, axis: number, dst?: Vec2): Vec2 {\n dst = dst || vec2.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n return dst;\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 */\nexport function setAxis(m: Mat3, v: Vec2, axis: number, dst?: Mat3): Mat3 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n return dst;\n}\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 */\nexport function getScaling(m: Mat3, dst?: Vec2): Vec2 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy);\n dst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return dst;\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 */\nexport function translation(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0;\n dst[ 8] = v[0]; dst[ 9] = v[1]; dst[10] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n }\n\n dst[ 8] = m00 * v0 + m10 * v1 + m20;\n dst[ 9] = m01 * v0 + m11 * v1 + m21;\n dst[10] = m02 * v0 + m12 * v1 + m22;\n\n return dst;\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 */\nexport function rotation(angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function rotate(m: Mat3, angleInRadians: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function scaling(v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat3, v: Vec2, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n const v0 = v[0];\n const v1 = v[1];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat3, s: number, dst?: Mat3): Mat3 {\n dst = dst || newMat3();\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n }\n\n return dst;\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 { Vec3, create, setDefaultType, VecType } from './vec3';\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\n\nexport default Vec3;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n\n return dst;\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 */\nexport function ceil(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n\n return dst;\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 */\nexport function floor(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n\n return dst;\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 */\nexport function round(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n\n return dst;\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 */\nexport function clamp(v: Vec3, min = 0, max = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n\n return dst;\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 */\nexport function add(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n\n return dst;\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 */\nexport function addScaled(a: Vec3, b: Vec3, scale: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n\n return dst;\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 */\nexport function angle(a: Vec3, b: Vec3): 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 */\nexport function subtract(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec3, b: Vec3): 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 */\nexport function equals(a: Vec3, b: Vec3): 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 */\nexport function lerp(a: Vec3, b: Vec3, t: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n\n return dst;\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 */\nexport function lerpV(a: Vec3, b: Vec3, t: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return dst;\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 */\nexport function max(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n\n return dst;\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 */\nexport function min(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec3, k: number, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function cross(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n dst[0] = a[1] * b[2] - a[2] * b[1];\n dst[1] = t1;\n dst[2] = t2;\n\n return dst;\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 */\nexport function dot(a: Vec3, b: Vec3): 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 */\nexport function length(v: Vec3): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec3): 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 */\nexport const 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 */\nexport function distance(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec3, b: Vec3): 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 */\nexport const 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 */\nexport function normalize(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n\n return dst;\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 */\nexport function negate(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n\n return dst;\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 */\nexport function copy(v: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec3, b: Vec3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n\n return dst;\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 */\nexport const 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 */\nexport function random(scale = 1, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = Math.cos(angle) * zScale;\n dst[1] = Math.sin(angle) * zScale;\n dst[2] = z * scale;\n\n return dst;\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 */\nexport function zero(dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n dst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n dst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return dst;\n}\n\n/**\n * Transform vec4 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 */\nexport function transformMat4Upper3x3(v: Vec3, m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n dst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n dst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return dst;\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 */\nexport function transformMat3(v: Vec3, m: Mat3, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n dst[0] = x * m[0] + y * m[4] + z * m[8];\n dst[1] = x * m[1] + y * m[5] + z * m[9];\n dst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return dst;\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 */\nexport function transformQuat(v: Vec3, q: Quat, dst?: Vec3): Vec3 {\n dst = dst || new VecType(3);\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 dst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n dst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n dst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return dst;\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 */\nexport function getTranslation(m: Mat3, dst?: Vec3) {\n dst = dst || new VecType(3);\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function getScaling(m: Mat4, dst: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return dst;\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 */\nexport function rotateX(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateY(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function rotateZ(a: Vec3, b: Vec3, rad: number, dst?: Vec3) {\n dst = dst || new VecType(3);\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 dst[0] = r[0] + b[0];\n dst[1] = r[1] + b[1];\n dst[2] = r[2] + b[2];\n\n return dst;\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 */\nexport function setLength(a: Vec3, len: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec3, maxLen: number, dst?: Vec3) {\n dst = dst || new VecType(3);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec3, b: Vec3, dst?: Vec3) {\n dst = dst || new VecType(3);\n return lerp(a, b, 0.5, dst);\n}\n","\nimport { Mat3 } from './mat3';\nimport { Mat4 } from './mat4';\nimport { Quat } from './quat';\nimport Vec3, * as vec3 from './vec3-impl';\nimport * as utils from './utils';\n\nexport default Mat4;\n\nexport type Mat4LikeCtor = new (n: number) => Mat4;\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `dst` 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 */\nlet MatType: Mat4LikeCtor = Float32Array;\n\n/**\n * Sets the type this library creates for a Mat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Mat4\n */\nexport function setDefaultType(ctor: new (n: number) => Mat4) {\n const oldType = MatType;\n MatType = ctor;\n return oldType;\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 * Note: a consequence of the implementation is if your Mat4Type = `Array`\n * instead of `Float32Array` or `Float64Array` then any values you\n * don't pass in will be undefined. Usually this is not an issue since\n * (a) using `Array` is rare and (b) using `mat4.create` is usually used\n * to create a Mat4 to be filled out as in\n *\n * ```\n * const m = mat4.create();\n * mat4.perspective(fov, aspect, near, far, m);\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 */\nexport function 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): Mat4 {\n const dst = new MatType(16);\n if (v0 !== undefined) {\n dst[0] = v0;\n if (v1 !== undefined) {\n dst[1] = v1;\n if (v2 !== undefined) {\n dst[2] = v2;\n if (v3 !== undefined) {\n dst[3] = v3;\n if (v4 !== undefined) {\n dst[4] = v4;\n if (v5 !== undefined) {\n dst[5] = v5;\n if (v6 !== undefined) {\n dst[6] = v6;\n if (v7 !== undefined) {\n dst[7] = v7;\n if (v8 !== undefined) {\n dst[8] = v8;\n if (v9 !== undefined) {\n dst[9] = v9;\n if (v10 !== undefined) {\n dst[10] = v10;\n if (v11 !== undefined) {\n dst[11] = v11;\n if (v12 !== undefined) {\n dst[12] = v12;\n if (v13 !== undefined) {\n dst[13] = v13;\n if (v14 !== undefined) {\n dst[14] = v14;\n if (v15 !== undefined) {\n dst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return dst;\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 */\nexport function 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?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v0; dst[ 1] = v1; dst[ 2] = v2; dst[ 3] = v3;\n dst[ 4] = v4; dst[ 5] = v5; dst[ 6] = v6; dst[ 7] = v7;\n dst[ 8] = v8; dst[ 9] = v9; dst[10] = v10; dst[11] = v11;\n dst[12] = v12; dst[13] = v13; dst[14] = v14; dst[15] = v15;\n\n return dst;\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 */\nexport function fromMat3(m3: Mat3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m3[0]; dst[ 1] = m3[1]; dst[ 2] = m3[ 2]; dst[ 3] = 0;\n dst[ 4] = m3[4]; dst[ 5] = m3[5]; dst[ 6] = m3[ 6]; dst[ 7] = 0;\n dst[ 8] = m3[8]; dst[ 9] = m3[9]; dst[10] = m3[10]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function fromQuat(q: Quat, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = 1 - yy - zz; dst[ 1] = yx + wz; dst[ 2] = zx - wy; dst[ 3] = 0;\n dst[ 4] = yx - wz; dst[ 5] = 1 - xx - zz; dst[ 6] = zy + wx; dst[ 7] = 0;\n dst[ 8] = zx + wy; dst[ 9] = zy - wx; dst[10] = 1 - xx - yy; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function negate(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = -m[ 0]; dst[ 1] = -m[ 1]; dst[ 2] = -m[ 2]; dst[ 3] = -m[ 3];\n dst[ 4] = -m[ 4]; dst[ 5] = -m[ 5]; dst[ 6] = -m[ 6]; dst[ 7] = -m[ 7];\n dst[ 8] = -m[ 8]; dst[ 9] = -m[ 9]; dst[10] = -m[10]; dst[11] = -m[11];\n dst[12] = -m[12]; dst[13] = -m[13]; dst[14] = -m[14]; dst[15] = -m[15];\n\n return dst;\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 */\nexport function copy(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = m[ 0]; dst[ 1] = m[ 1]; dst[ 2] = m[ 2]; dst[ 3] = m[ 3];\n dst[ 4] = m[ 4]; dst[ 5] = m[ 5]; dst[ 6] = m[ 6]; dst[ 7] = m[ 7];\n dst[ 8] = m[ 8]; dst[ 9] = m[ 9]; dst[10] = m[10]; dst[11] = m[11];\n dst[12] = m[12]; dst[13] = m[13]; dst[14] = m[14]; dst[15] = m[15];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Mat4, b: Mat4): 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 */\nexport function equals(a: Mat4, b: Mat4): 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 */\nexport function identity(dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function transpose(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n if (dst === 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 dst;\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 dst[ 0] = m00; dst[ 1] = m10; dst[ 2] = m20; dst[ 3] = m30;\n dst[ 4] = m01; dst[ 5] = m11; dst[ 6] = m21; dst[ 7] = m31;\n dst[ 8] = m02; dst[ 9] = m12; dst[10] = m22; dst[11] = m32;\n dst[12] = m03; dst[13] = m13; dst[14] = m23; dst[15] = m33;\n\n return dst;\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 */\nexport function inverse(m: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = d * t0;\n dst[ 1] = d * t1;\n dst[ 2] = d * t2;\n dst[ 3] = d * t3;\n dst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n dst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n dst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n dst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n dst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n dst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n dst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n dst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n dst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n dst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n dst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n dst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return dst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nexport function determinant(m: Mat4): 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 */\nexport const 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 */\nexport function multiply(a: Mat4, b: Mat4, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n dst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n dst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n dst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n dst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n dst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n dst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n dst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n dst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n dst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n dst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n dst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n dst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n dst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n dst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n dst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return dst;\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 */\nexport const 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 */\nexport function setTranslation(a: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || identity();\n if (a !== dst) {\n dst[ 0] = a[ 0];\n dst[ 1] = a[ 1];\n dst[ 2] = a[ 2];\n dst[ 3] = a[ 3];\n dst[ 4] = a[ 4];\n dst[ 5] = a[ 5];\n dst[ 6] = a[ 6];\n dst[ 7] = a[ 7];\n dst[ 8] = a[ 8];\n dst[ 9] = a[ 9];\n dst[10] = a[10];\n dst[11] = a[11];\n }\n dst[12] = v[0];\n dst[13] = v[1];\n dst[14] = v[2];\n dst[15] = 1;\n return dst;\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 */\nexport function getTranslation(m: Mat4, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n dst[0] = m[12];\n dst[1] = m[13];\n dst[2] = m[14];\n return dst;\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 */\nexport function getAxis(m: Mat4, axis: number, dst?: Vec3): Vec3 {\n dst = dst || vec3.create();\n const off = axis * 4;\n dst[0] = m[off + 0];\n dst[1] = m[off + 1];\n dst[2] = m[off + 2];\n return dst;\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 */\nexport function setAxis(m: Mat4, v: Vec3, axis: number, dst: Mat4): Mat4 {\n if (dst !== m) {\n dst = copy(m, dst);\n }\n const off = axis * 4;\n dst[off + 0] = v[0];\n dst[off + 1] = v[1];\n dst[off + 2] = v[2];\n return dst;\n}\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 */\nexport function getScaling(m: Mat4, dst?: Vec3): Vec3 {\n dst = 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 dst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n dst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n dst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return dst;\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 */\nexport function perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n dst[0] = f / aspect;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = f;\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n dst[10] = zFar * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n } else {\n dst[10] = -1;\n dst[14] = -zNear;\n }\n\n return dst;\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 */export function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: Mat4) {\n dst = dst || new MatType(16);\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n dst[ 0] = f / aspect;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n\n dst[ 4] = 0;\n dst[ 5] = f;\n dst[ 6] = 0;\n dst[ 7] = 0;\n\n dst[ 8] = 0;\n dst[ 9] = 0;\n dst[11] = -1;\n\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (zFar === Infinity) {\n dst[10] = 0;\n dst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n dst[10] = zNear * rangeInv;\n dst[14] = zFar * zNear * rangeInv;\n }\n\n return dst;\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 */\nexport function ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[0] = 2 / (right - left);\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n dst[4] = 0;\n dst[5] = 2 / (top - bottom);\n dst[6] = 0;\n dst[7] = 0;\n\n dst[8] = 0;\n dst[9] = 0;\n dst[10] = 1 / (near - far);\n dst[11] = 0;\n\n dst[12] = (right + left) / (left - right);\n dst[13] = (top + bottom) / (bottom - top);\n dst[14] = near / (near - far);\n dst[15] = 1;\n\n return dst;\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 */\nexport function frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[10] = far / dz;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = near * far / dz;\n dst[15] = 0;\n\n return dst;\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 */\nexport function frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n dst[ 0] = 2 * near / dx;\n dst[ 1] = 0;\n dst[ 2] = 0;\n dst[ 3] = 0;\n dst[ 4] = 0;\n dst[ 5] = 2 * near / dy;\n dst[ 6] = 0;\n dst[ 7] = 0;\n dst[ 8] = (left + right) / dx;\n dst[ 9] = (top + bottom) / dy;\n dst[11] = -1;\n dst[12] = 0;\n dst[13] = 0;\n dst[15] = 0;\n\n if (far === Infinity) {\n dst[10] = 0;\n dst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n dst[10] = near * rangeInv;\n dst[14] = far * near * rangeInv;\n }\n\n return dst;\n}\n\nlet xAxis: Vec3;\nlet yAxis: Vec3;\nlet zAxis: Vec3;\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 */\nexport function aim(position: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = position[0]; dst[13] = position[1]; dst[14] = position[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function cameraAim(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = xAxis[1]; dst[ 2] = xAxis[2]; dst[ 3] = 0;\n dst[ 4] = yAxis[0]; dst[ 5] = yAxis[1]; dst[ 6] = yAxis[2]; dst[ 7] = 0;\n dst[ 8] = zAxis[0]; dst[ 9] = zAxis[1]; dst[10] = zAxis[2]; dst[11] = 0;\n dst[12] = eye[0]; dst[13] = eye[1]; dst[14] = eye[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function lookAt(eye: Vec3, target: Vec3, up: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n xAxis = xAxis || vec3.create();\n yAxis = yAxis || vec3.create();\n zAxis = zAxis || vec3.create();\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 dst[ 0] = xAxis[0]; dst[ 1] = yAxis[0]; dst[ 2] = zAxis[0]; dst[ 3] = 0;\n dst[ 4] = xAxis[1]; dst[ 5] = yAxis[1]; dst[ 6] = zAxis[1]; dst[ 7] = 0;\n dst[ 8] = xAxis[2]; dst[ 9] = yAxis[2]; dst[10] = zAxis[2]; dst[11] = 0;\n\n dst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n dst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n dst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n dst[15] = 1;\n\n return dst;\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 */\nexport function translation(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = v[0]; dst[13] = v[1]; dst[14] = v[2]; dst[15] = 1;\n\n return dst;\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 */\nexport function translate(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 !== dst) {\n dst[ 0] = m00;\n dst[ 1] = m01;\n dst[ 2] = m02;\n dst[ 3] = m03;\n dst[ 4] = m10;\n dst[ 5] = m11;\n dst[ 6] = m12;\n dst[ 7] = m13;\n dst[ 8] = m20;\n dst[ 9] = m21;\n dst[10] = m22;\n dst[11] = m23;\n }\n\n dst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n dst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n dst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n dst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return dst;\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 */\nexport function rotationX(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = 1; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = c; dst[ 6] = s; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = -s; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateX(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[4] = c * m10 + s * m20;\n dst[5] = c * m11 + s * m21;\n dst[6] = c * m12 + s * m22;\n dst[7] = c * m13 + s * m23;\n dst[8] = c * m20 - s * m10;\n dst[9] = c * m21 - s * m11;\n dst[10] = c * m22 - s * m12;\n dst[11] = c * m23 - s * m13;\n\n if (m !== dst) {\n dst[ 0] = m[ 0];\n dst[ 1] = m[ 1];\n dst[ 2] = m[ 2];\n dst[ 3] = m[ 3];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationY(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = 0; dst[ 2] = -s; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = 1; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = s; dst[ 9] = 0; dst[10] = c; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateY(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 - s * m20;\n dst[ 1] = c * m01 - s * m21;\n dst[ 2] = c * m02 - s * m22;\n dst[ 3] = c * m03 - s * m23;\n dst[ 8] = c * m20 + s * m00;\n dst[ 9] = c * m21 + s * m01;\n dst[10] = c * m22 + s * m02;\n dst[11] = c * m23 + s * m03;\n\n if (m !== dst) {\n dst[ 4] = m[ 4];\n dst[ 5] = m[ 5];\n dst[ 6] = m[ 6];\n dst[ 7] = m[ 7];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function rotationZ(angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n dst[ 0] = c; dst[ 1] = s; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = -s; dst[ 5] = c; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = 1; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function rotateZ(m: Mat4, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = c * m00 + s * m10;\n dst[ 1] = c * m01 + s * m11;\n dst[ 2] = c * m02 + s * m12;\n dst[ 3] = c * m03 + s * m13;\n dst[ 4] = c * m10 - s * m00;\n dst[ 5] = c * m11 - s * m01;\n dst[ 6] = c * m12 - s * m02;\n dst[ 7] = c * m13 - s * m03;\n\n if (m !== dst) {\n dst[ 8] = m[ 8];\n dst[ 9] = m[ 9];\n dst[10] = m[10];\n dst[11] = m[11];\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function axisRotation(axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = xx + (1 - xx) * c;\n dst[ 1] = x * y * oneMinusCosine + z * s;\n dst[ 2] = x * z * oneMinusCosine - y * s;\n dst[ 3] = 0;\n dst[ 4] = x * y * oneMinusCosine - z * s;\n dst[ 5] = yy + (1 - yy) * c;\n dst[ 6] = y * z * oneMinusCosine + x * s;\n dst[ 7] = 0;\n dst[ 8] = x * z * oneMinusCosine + y * s;\n dst[ 9] = y * z * oneMinusCosine - x * s;\n dst[10] = zz + (1 - zz) * c;\n dst[11] = 0;\n dst[12] = 0;\n dst[13] = 0;\n dst[14] = 0;\n dst[15] = 1;\n\n return dst;\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 */\nexport const 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 */\nexport function axisRotate(m: Mat4, axis: Vec3, angleInRadians: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\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 dst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n dst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n dst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n dst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n dst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n dst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n dst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n dst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n dst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n dst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n dst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n dst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport const 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 */\nexport function scaling(v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = v[0]; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = v[1]; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = v[2]; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function scale(m: Mat4, v: Vec3, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n dst[ 0] = v0 * m[0 * 4 + 0];\n dst[ 1] = v0 * m[0 * 4 + 1];\n dst[ 2] = v0 * m[0 * 4 + 2];\n dst[ 3] = v0 * m[0 * 4 + 3];\n dst[ 4] = v1 * m[1 * 4 + 0];\n dst[ 5] = v1 * m[1 * 4 + 1];\n dst[ 6] = v1 * m[1 * 4 + 2];\n dst[ 7] = v1 * m[1 * 4 + 3];\n dst[ 8] = v2 * m[2 * 4 + 0];\n dst[ 9] = v2 * m[2 * 4 + 1];\n dst[10] = v2 * m[2 * 4 + 2];\n dst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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 */\nexport function uniformScaling(s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s; dst[ 1] = 0; dst[ 2] = 0; dst[ 3] = 0;\n dst[ 4] = 0; dst[ 5] = s; dst[ 6] = 0; dst[ 7] = 0;\n dst[ 8] = 0; dst[ 9] = 0; dst[10] = s; dst[11] = 0;\n dst[12] = 0; dst[13] = 0; dst[14] = 0; dst[15] = 1;\n\n return dst;\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 */\nexport function uniformScale(m: Mat4, s: number, dst?: Mat4): Mat4 {\n dst = dst || new MatType(16);\n\n dst[ 0] = s * m[0 * 4 + 0];\n dst[ 1] = s * m[0 * 4 + 1];\n dst[ 2] = s * m[0 * 4 + 2];\n dst[ 3] = s * m[0 * 4 + 3];\n dst[ 4] = s * m[1 * 4 + 0];\n dst[ 5] = s * m[1 * 4 + 1];\n dst[ 6] = s * m[1 * 4 + 2];\n dst[ 7] = s * m[1 * 4 + 3];\n dst[ 8] = s * m[2 * 4 + 0];\n dst[ 9] = s * m[2 * 4 + 1];\n dst[10] = s * m[2 * 4 + 2];\n dst[11] = s * m[2 * 4 + 3];\n\n if (m !== dst) {\n dst[12] = m[12];\n dst[13] = m[13];\n dst[14] = m[14];\n dst[15] = m[15];\n }\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link quat.setDefaultType}.\n */\nexport type Quat = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let QuatType: new (n: number) => Quat = Float32Array;\n\n/**\n * Sets the type this library creates for a Quat4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Quat4\n */\nexport function setDefaultType(ctor: new (n: number) => Quat) {\n const oldType = QuatType;\n QuatType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Quat {\n const dst = new QuatType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Quat, create, setDefaultType, QuatType } from './quat';\nimport { Mat3 } from './mat3.js';\nimport { Mat4 } from './mat4.js';\nimport { Vec3 } from './vec3.js';\nimport * as vec3 from './vec3-impl.js';\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\nexport default Quat;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Quat) {\n dst = dst || new QuatType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 **/\nexport function fromAxisAngle(axis: Vec3, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n dst[0] = s * axis[0];\n dst[1] = s * axis[1];\n dst[2] = s * axis[2];\n dst[3] = Math.cos(halfAngle);\n\n return dst;\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 */\nexport function toAxisAngle(q: Quat, dst?: Vec3): { angle: number, axis: Vec3 } {\n dst = dst || vec3.create(4);\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n dst[0] = q[0] / s;\n dst[1] = q[1] / s;\n dst[2] = q[2] / s;\n } else {\n dst[0] = 1;\n dst[1] = 0;\n dst[2] = 0;\n }\n\n return { angle, axis: dst };\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 */\nexport function angle(a: Quat, b: Quat) {\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 */\nexport function multiply(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = ax * bw + aw * bx + ay * bz - az * by;\n dst[1] = ay * bw + aw * by + az * bx - ax * bz;\n dst[2] = az * bw + aw * bz + ax * by - ay * bx;\n dst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return dst;\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 */\nexport const 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 */\nexport function rotateX(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qw * bx;\n dst[1] = qy * bw + qz * bx;\n dst[2] = qz * bw - qy * bx;\n dst[3] = qw * bw - qx * bx;\n\n return dst;\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 */\nexport function rotateY(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw - qz * by;\n dst[1] = qy * bw + qw * by;\n dst[2] = qz * bw + qx * by;\n dst[3] = qw * bw - qy * by;\n\n return dst;\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 */\nexport function rotateZ(q: Quat, angleInRadians: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = qx * bw + qy * bz;\n dst[1] = qy * bw - qx * bz;\n dst[2] = qz * bw + qw * bz;\n dst[3] = qw * bw - qz * bz;\n\n return dst;\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 */\nexport function slerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = scale0 * ax + scale1 * bx;\n dst[1] = scale0 * ay + scale1 * by;\n dst[2] = scale0 * az + scale1 * bz;\n dst[3] = scale0 * aw + scale1 * bw;\n\n return dst;\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 */\nexport function inverse(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = -a0 * invDot;\n dst[1] = -a1 * invDot;\n dst[2] = -a2 * invDot;\n dst[3] = a3 * invDot;\n\n return dst;\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 */\nexport function conjugate(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = -q[0];\n dst[1] = -q[1];\n dst[2] = -q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport function fromMat(m: Mat3 | Mat4, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n dst[0] = (m[6] - m[9]) * invRoot;\n dst[1] = (m[8] - m[2]) * invRoot;\n dst[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 dst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n dst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n dst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n dst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return dst;\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 */\nexport function fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: Quat) {\n dst = dst || new QuatType(4);\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 dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz - sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n dst[0] = sx * cy * cz + cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz + sx * sy * cz;\n dst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n dst[0] = sx * cy * cz - cx * sy * sz;\n dst[1] = cx * sy * cz + sx * cy * sz;\n dst[2] = cx * cy * sz - sx * sy * cz;\n dst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return dst;\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 */\nexport function copy(q: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = q[0];\n dst[1] = q[1];\n dst[2] = q[2];\n dst[3] = q[3];\n\n return dst;\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 */\nexport const 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 */\nexport function add(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function subtract(a: Quat, b: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function mulScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Quat, k: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function dot(a: Quat, b: Quat): 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 */\nexport function lerp(a: Quat, b: Quat, t: number, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nexport function length(v: Quat): 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 */\nexport const 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 */\nexport function lengthSq(v: Quat): 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 */\nexport const 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 */\nexport function normalize(v: Quat, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function equalsApproximately(a: Quat, b: Quat): 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 */\nexport function equals(a: Quat, b: Quat): 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 */\nexport function identity(dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n}\n\nlet tempVec3: Vec3;\nlet xUnitVec3: Vec3;\nlet yUnitVec3: Vec3;\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 */\nexport function rotationTo(aUnit: Vec3, bUnit: Vec3, dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempVec3 = tempVec3 || vec3.create();\n xUnitVec3 = xUnitVec3 || vec3.create(1, 0, 0);\n yUnitVec3 = yUnitVec3 || vec3.create(0, 1, 0);\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, dst);\n\n return dst;\n } else if (dot > 0.999999) {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 1;\n\n return dst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n dst[0] = tempVec3[0];\n dst[1] = tempVec3[1];\n dst[2] = tempVec3[2];\n dst[3] = 1 + dot;\n\n return normalize(dst, dst);\n }\n}\n\nlet tempQuat1: Quat;\nlet tempQuat2: Quat;\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 */\nexport function sqlerp(\n a: Quat,\n b: Quat,\n c: Quat,\n d: Quat,\n t: number,\n dst?: Quat): Quat {\n dst = dst || new QuatType(4);\n\n tempQuat1 = tempQuat1 || new QuatType(4);\n tempQuat2 = tempQuat2 || new QuatType(4);\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), dst);\n\n return dst;\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\n/**\n * A JavaScript array with 4 values, Float32Array with 4 values, or a Float64Array with 4 values.\n * When created by the library will create the default type which is `Float32Array`\n * but can be set by calling {@link vec4.setDefaultType}.\n */\nexport type Vec4 = number[] | Float32Array | Float64Array;\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `dst` 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 */\n\nexport let VecType: new (n: number) => Vec4 = Float32Array;\n\n/**\n * Sets the type this library creates for a Vec4\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n * @returns previous constructor for Vec4\n */\nexport function setDefaultType(ctor: new (n: number) => Vec4) {\n const oldType = VecType;\n VecType = ctor;\n return oldType;\n}\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 */\nexport function create(x?: number, y?: number, z?: number, w?: number): Vec4 {\n const dst = new VecType(4);\n if (x !== undefined) {\n dst[0] = x;\n if (y !== undefined) {\n dst[1] = y;\n if (z !== undefined) {\n dst[2] = z;\n if (w !== undefined) {\n dst[3] = w;\n }\n }\n }\n }\n return dst;\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 { Vec4, create, setDefaultType, VecType } from './vec4';\nimport { Mat4 } from './mat4';\n\nexport default Vec4;\nexport { create, setDefaultType };\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 */\nexport const 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 */\nexport function set(x: number, y: number, z: number, w: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = x;\n dst[1] = y;\n dst[2] = z;\n dst[3] = w;\n\n return dst;\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 */\nexport function ceil(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.ceil(v[0]);\n dst[1] = Math.ceil(v[1]);\n dst[2] = Math.ceil(v[2]);\n dst[3] = Math.ceil(v[3]);\n\n return dst;\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 */\nexport function floor(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.floor(v[0]);\n dst[1] = Math.floor(v[1]);\n dst[2] = Math.floor(v[2]);\n dst[3] = Math.floor(v[3]);\n\n return dst;\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 */\nexport function round(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.round(v[0]);\n dst[1] = Math.round(v[1]);\n dst[2] = Math.round(v[2]);\n dst[3] = Math.round(v[3]);\n\n return dst;\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 */\nexport function clamp(v: Vec4, min = 0, max = 1, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(max, Math.max(min, v[0]));\n dst[1] = Math.min(max, Math.max(min, v[1]));\n dst[2] = Math.min(max, Math.max(min, v[2]));\n dst[3] = Math.min(max, Math.max(min, v[3]));\n\n return dst;\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 */\nexport function add(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0];\n dst[1] = a[1] + b[1];\n dst[2] = a[2] + b[2];\n dst[3] = a[3] + b[3];\n\n return dst;\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 */\nexport function addScaled(a: Vec4, b: Vec4, scale: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + b[0] * scale;\n dst[1] = a[1] + b[1] * scale;\n dst[2] = a[2] + b[2] * scale;\n dst[3] = a[3] + b[3] * scale;\n\n return dst;\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 */\nexport function subtract(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] - b[0];\n dst[1] = a[1] - b[1];\n dst[2] = a[2] - b[2];\n dst[3] = a[3] - b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function equalsApproximately(a: Vec4, b: Vec4): 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 */\nexport function equals(a: Vec4, b: Vec4): 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 */\nexport function lerp(a: Vec4, b: Vec4, t: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t * (b[0] - a[0]);\n dst[1] = a[1] + t * (b[1] - a[1]);\n dst[2] = a[2] + t * (b[2] - a[2]);\n dst[3] = a[3] + t * (b[3] - a[3]);\n\n return dst;\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 */\nexport function lerpV(a: Vec4, b: Vec4, t: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] + t[0] * (b[0] - a[0]);\n dst[1] = a[1] + t[1] * (b[1] - a[1]);\n dst[2] = a[2] + t[2] * (b[2] - a[2]);\n dst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return dst;\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 */\nexport function max(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.max(a[0], b[0]);\n dst[1] = Math.max(a[1], b[1]);\n dst[2] = Math.max(a[2], b[2]);\n dst[3] = Math.max(a[3], b[3]);\n\n return dst;\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 */\nexport function min(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = Math.min(a[0], b[0]);\n dst[1] = Math.min(a[1], b[1]);\n dst[2] = Math.min(a[2], b[2]);\n dst[3] = Math.min(a[3], b[3]);\n\n return dst;\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 */\nexport function mulScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] * k;\n dst[1] = v[1] * k;\n dst[2] = v[2] * k;\n dst[3] = v[3] * k;\n\n return dst;\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 */\nexport const 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 */\nexport function divScalar(v: Vec4, k: number, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0] / k;\n dst[1] = v[1] / k;\n dst[2] = v[2] / k;\n dst[3] = v[3] / k;\n\n return dst;\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 */\nexport function inverse(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 1 / v[0];\n dst[1] = 1 / v[1];\n dst[2] = 1 / v[2];\n dst[3] = 1 / v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function dot(a: Vec4, b: Vec4): 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 */\nexport function length(v: Vec4): 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 */\nexport const 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 */\nexport function lengthSq(v: Vec4): 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 */\nexport const 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 */\nexport function distance(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function distanceSq(a: Vec4, b: Vec4): 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 */\nexport const 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 */\nexport function normalize(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\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 dst[0] = v0 / len;\n dst[1] = v1 / len;\n dst[2] = v2 / len;\n dst[3] = v3 / len;\n } else {\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n }\n\n return dst;\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 */\nexport function negate(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = -v[0];\n dst[1] = -v[1];\n dst[2] = -v[2];\n dst[3] = -v[3];\n\n return dst;\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 */\nexport function copy(v: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = v[0];\n dst[1] = v[1];\n dst[2] = v[2];\n dst[3] = v[3];\n\n return dst;\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 */\nexport const 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 */\nexport function multiply(a: Vec4, b: Vec4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] * b[0];\n dst[1] = a[1] * b[1];\n dst[2] = a[2] * b[2];\n dst[3] = a[3] * b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function divide(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n dst[0] = a[0] / b[0];\n dst[1] = a[1] / b[1];\n dst[2] = a[2] / b[2];\n dst[3] = a[3] / b[3];\n\n return dst;\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 */\nexport const 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 */\nexport function zero(dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n dst[0] = 0;\n dst[1] = 0;\n dst[2] = 0;\n dst[3] = 0;\n\n return dst;\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 */\nexport function transformMat4(v: Vec4, m: Mat4, dst?: Vec4): Vec4 {\n dst = dst || new VecType(4);\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n dst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n dst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n dst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n dst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return dst;\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 */\nexport function setLength(a: Vec4, len: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n normalize(a, dst);\n return mulScalar(dst, len, dst);\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 */\nexport function truncate(a: Vec4, maxLen: number, dst?: Vec4) {\n dst = dst || new VecType(4);\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, dst);\n }\n\n return copy(a, dst);\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 */\nexport function midpoint(a: Vec4, b: Vec4, dst?: Vec4) {\n dst = dst || new VecType(4);\n return lerp(a, b, 0.5, dst);\n}\n","import Mat3, * as mat3 from './mat3-impl';\nimport Mat4, * as mat4 from './mat4-impl';\nimport Quat, * as quat from './quat-impl';\nimport Vec2, * as vec2 from './vec2-impl';\nimport Vec3, * as vec3 from './vec3-impl';\nimport Vec4, * as vec4 from './vec4-impl';\nimport * as utils from './utils';\n\n/**\n * Sets the type this library creates for all types\n *\n * example:\n *\n * ```\n * setDefaultType(Float64Array);\n * ```\n *\n * @param ctor - the constructor for the type. Either `Float32Array`, `Float64Array`, or `Array`\n */\nexport function setDefaultType(ctor: new (n: number) => Float32Array | Float64Array | number[]) {\n mat3.setDefaultType(ctor);\n mat4.setDefaultType(ctor);\n quat.setDefaultType(ctor);\n vec2.setDefaultType(ctor);\n vec3.setDefaultType(ctor);\n vec4.setDefaultType(ctor);\n}\n\nexport {\n Mat3,\n mat3,\n Mat4,\n mat4,\n Quat,\n quat,\n utils,\n Vec2,\n vec2,\n Vec3,\n vec3,\n Vec4,\n 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\ No newline at end of file diff --git a/docs/functions/mat4.frustumReverseZ.html b/docs/functions/mat4.frustumReverseZ.html new file mode 100644 index 0000000..1fb81b0 --- /dev/null +++ b/docs/functions/mat4.frustumReverseZ.html @@ -0,0 +1,17 @@ +frustumReverseZ | wgpu-matrix

Function frustumReverseZ

  • frustumReverseZ(left, right, bottom, top, near, far?, dst?): Mat4

  • Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right, +top, bottom, near and far clipping planes. The arguments define a frustum +extending in the negative z direction. The arguments near and far are the +distances to the near and far clipping planes. Note that near and far are not +z coordinates, but rather they are distances along the negative z-axis. The +matrix generated sends the viewing frustum to the unit box. We assume a unit +box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z +dimension.

    +

    Parameters

    • left: number

      The x coordinate of the left plane of the box.

      +
    • right: number

      The x coordinate of the right plane of the box.

      +
    • bottom: number

      The y coordinate of the bottom plane of the box.

      +
    • top: number

      The y coordinate of the right plane of the box.

      +
    • near: number

      The negative z coordinate of the near plane of the box.

      +
    • far: number = Infinity

      The negative z coordinate of the far plane of the box.

      +
    • Optional dst: Mat4

      Output matrix. If not passed a new one is created.

      +

    Returns Mat4

    The perspective projection matrix.

    +

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\ No newline at end of file diff --git a/docs/functions/mat4.perspectiveReverseZ.html b/docs/functions/mat4.perspectiveReverseZ.html new file mode 100644 index 0000000..a155f89 --- /dev/null +++ b/docs/functions/mat4.perspectiveReverseZ.html @@ -0,0 +1,19 @@ +perspectiveReverseZ | wgpu-matrix

Function perspectiveReverseZ

  • perspectiveReverseZ(fieldOfViewYInRadians, aspect, zNear, zFar?, dst?): Mat4

  • Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height +of the frustum, the aspect ratio, and the near and far clipping planes. The +arguments define a frustum extending in the negative z direction. The given +angle is the vertical angle of the frustum, and the horizontal angle is +determined to produce the given aspect ratio. The arguments near and far are +the distances to the near and far clipping planes. Note that near and far +are not z coordinates, but rather they are distances along the negative +z-axis. The matrix generated sends the viewing frustum to the unit box. +We assume a unit box extending from -1 to 1 in the x and y dimensions and +from 1 (at -zNear) to 0 (at -zFar) in the z dimension.

    +

    Parameters

    • fieldOfViewYInRadians: number

      The camera angle from top to bottom (in radians).

      +
    • aspect: number

      The aspect ratio width / height.

      +
    • zNear: number

      The depth (negative z coordinate) + of the near clipping plane.

      +
    • zFar: number = Infinity

      The depth (negative z coordinate) + of the far clipping plane. (default = Infinity)

      +
    • Optional dst: Mat4

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

      +

    Returns Mat4

    The perspective matrix.

    +

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\ No newline at end of file diff --git a/docs/modules/mat4.html b/docs/modules/mat4.html index 1c3db1d..f6a0c6f 100644 --- a/docs/modules/mat4.html +++ b/docs/modules/mat4.html @@ -13,6 +13,7 @@ fromMat3 fromQuat frustum +frustumReverseZ getAxis getScaling getTranslation @@ -25,6 +26,7 @@ negate ortho perspective +perspectiveReverseZ rotate rotateX rotateY diff --git a/package-lock.json b/package-lock.json index f2ccebb..e931ed7 100644 --- a/package-lock.json +++ b/package-lock.json @@ -1,12 +1,12 @@ { "name": "wgpu-matrix", - "version": "2.8.3", + "version": "2.9.0", "lockfileVersion": 3, "requires": true, "packages": { "": { "name": "wgpu-matrix", - "version": "2.8.3", + "version": "2.9.0", "license": "MIT", "devDependencies": { "@rollup/plugin-typescript": "^11.1.6", diff --git a/package.json b/package.json index 3cdb50d..04e43aa 100644 --- a/package.json +++ b/package.json @@ -1,6 +1,6 @@ { "name": "wgpu-matrix", - "version": "2.8.3", + "version": "2.9.0", "description": "fast matrix math library for WebGPU", "main": "dist/2.x/wgpu-matrix.module.js", "module": "dist/2.x/wgpu-matrix.module.js", diff --git a/src/mat4-impl.ts b/src/mat4-impl.ts index b26db8a..a5c4a2e 100644 --- a/src/mat4-impl.ts +++ b/src/mat4-impl.ts @@ -776,12 +776,67 @@ export function perspective(fieldOfViewYInRadians: number, aspect: number, zNear dst[13] = 0; dst[15] = 0; - if (zFar === Infinity) { + if (Number.isFinite(zFar)) { + const rangeInv = 1 / (zNear - zFar); + dst[10] = zFar * rangeInv; + dst[14] = zFar * zNear * rangeInv; + } else { dst[10] = -1; dst[14] = -zNear; + } + + return dst; +} + +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height + * of the frustum, the aspect ratio, and the near and far clipping planes. The + * arguments define a frustum extending in the negative z direction. The given + * angle is the vertical angle of the frustum, and the horizontal angle is + * determined to produce the given aspect ratio. The arguments near and far are + * the distances to the near and far clipping planes. Note that near and far + * are not z coordinates, but rather they are distances along the negative + * z-axis. The matrix generated sends the viewing frustum to the unit box. + * We assume a unit box extending from -1 to 1 in the x and y dimensions and + * from 1 (at -zNear) to 0 (at -zFar) in the z dimension. + * + * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians). + * @param aspect - The aspect ratio width / height. + * @param zNear - The depth (negative z coordinate) + * of the near clipping plane. + * @param zFar - The depth (negative z coordinate) + * of the far clipping plane. (default = Infinity) + * @param dst - matrix to hold result. If not passed a new one is created. + * @returns The perspective matrix. + */export function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: Mat4) { + dst = dst || new MatType(16); + + const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5); + + dst[ 0] = f / aspect; + dst[ 1] = 0; + dst[ 2] = 0; + dst[ 3] = 0; + + dst[ 4] = 0; + dst[ 5] = f; + dst[ 6] = 0; + dst[ 7] = 0; + + dst[ 8] = 0; + dst[ 9] = 0; + dst[11] = -1; + + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + + if (zFar === Infinity) { + dst[10] = 0; + dst[14] = zNear; } else { - const rangeInv = 1 / (zNear - zFar); - dst[10] = zFar * rangeInv; + const rangeInv = 1 / (zFar - zNear); + dst[10] = zNear * rangeInv; dst[14] = zFar * zNear * rangeInv; } @@ -874,6 +929,57 @@ export function frustum(left: number, right: number, bottom: number, top: number return dst; } +/** + * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right, + * top, bottom, near and far clipping planes. The arguments define a frustum + * extending in the negative z direction. The arguments near and far are the + * distances to the near and far clipping planes. Note that near and far are not + * z coordinates, but rather they are distances along the negative z-axis. The + * matrix generated sends the viewing frustum to the unit box. We assume a unit + * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z + * dimension. + * @param left - The x coordinate of the left plane of the box. + * @param right - The x coordinate of the right plane of the box. + * @param bottom - The y coordinate of the bottom plane of the box. + * @param top - The y coordinate of the right plane of the box. + * @param near - The negative z coordinate of the near plane of the box. + * @param far - The negative z coordinate of the far plane of the box. + * @param dst - Output matrix. If not passed a new one is created. + * @returns The perspective projection matrix. + */ +export function frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: Mat4): Mat4 { + dst = dst || new MatType(16); + + const dx = (right - left); + const dy = (top - bottom); + + dst[ 0] = 2 * near / dx; + dst[ 1] = 0; + dst[ 2] = 0; + dst[ 3] = 0; + dst[ 4] = 0; + dst[ 5] = 2 * near / dy; + dst[ 6] = 0; + dst[ 7] = 0; + dst[ 8] = (left + right) / dx; + dst[ 9] = (top + bottom) / dy; + dst[11] = -1; + dst[12] = 0; + dst[13] = 0; + dst[15] = 0; + + if (far === Infinity) { + dst[10] = 0; + dst[14] = near; + } else { + const rangeInv = 1 / (far - near); + dst[10] = near * rangeInv; + dst[14] = far * near * rangeInv; + } + + return dst; +} + let xAxis: Vec3; let yAxis: Vec3; let zAxis: Vec3; diff --git a/test/tests/mat4-test.js b/test/tests/mat4-test.js index d4494ad..58f7050 100644 --- a/test/tests/mat4-test.js +++ b/test/tests/mat4-test.js @@ -474,6 +474,95 @@ function check(Type) { shouldBeCloseArray(vec3.transformMat4([0, 0, zFar], m), [0, 0, Infinity], 0.000001); }); + it('should compute perspective reverseZ with zFar', () => { + const fov = 2; + const aspect = 4; + const zNear = 10; + const zFar = 20; + const f = Math.tan(Math.PI * 0.5 - 0.5 * fov); + const rangeInv = 1 / (zFar - zNear); + const expected = [ + f / aspect, + 0, + 0, + 0, + + 0, + f, + 0, + 0, + + 0, + 0, + zNear * rangeInv, + -1, + + 0, + 0, + zFar * zNear * rangeInv, + 0, + ]; + testMat4WithAndWithoutDest((dst) => { + return mat4.perspectiveReverseZ(fov, aspect, zNear, zFar, dst); + }, expected); + }); + + it('should compute correct perspective reverseZ', () => { + const fov = Math.PI / 4; + const aspect = 2; + const zNear = 10; + const zFar = 20; + const m = mat4.perspectiveReverseZ(fov, aspect, zNear, zFar); + shouldBeCloseArray(vec3.transformMat4([0, 0, -zNear], m), [0, 0, 1], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -15], m), [0, 0, 0.3333333432674408], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -zFar], m), [0, 0, 0], 0.000001); + }); + + it('should compute perspective reverseZ with zFar at infinity', () => { + const fov = 2; + const aspect = 4; + const zNear = 10; + const zFar = Infinity; + const f = Math.tan(Math.PI * 0.5 - 0.5 * fov); + const expected = [ + f / aspect, + 0, + 0, + 0, + + 0, + f, + 0, + 0, + + 0, + 0, + 0, + -1, + + 0, + 0, + zNear, + 0, + ]; + testMat4WithAndWithoutDest((dst) => { + return mat4.perspectiveReverseZ(fov, aspect, zNear, zFar, dst); + }, expected); + }); + + it('should compute correct perspective reverseZ with zFar at Infinity', () => { + const fov = Math.PI / 4; + const aspect = 2; + const zNear = 10; + const zFar = Infinity; + const m = mat4.perspectiveReverseZ(fov, aspect, zNear, zFar); + shouldBeCloseArray(vec3.transformMat4([0, 0, -zNear], m), [0, 0, 1], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -1000], m), [0, 0, 0.009999999776482582], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -1000000], m), [0, 0, 0.000009999999747378752], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -1000000000], m), [0, 0, 9.99999993922529e-9], 0.000001); + shouldBeCloseArray(vec3.transformMat4([0, 0, -zFar], m), [0, 0, 0], 0.000001); + }); + it('should compute ortho', () => { const left = 2; const right = 4; @@ -570,6 +659,56 @@ function check(Type) { assertEqualApproximately(p[2], 1); }); + it('should compute frustumReverseZ', () => { + const left = 2; + const right = 4; + const top = 10; + const bottom = 30; + const near = 15; + const far = 25; + + const dx = (right - left); + const dy = (top - bottom); + const dz = (far - near); + + const expected = [ + 2 * near / dx, + 0, + 0, + 0, + 0, + 2 * near / dy, + 0, + 0, + (left + right) / dx, + (top + bottom) / dy, + near / dz, + -1, + 0, + 0, + near * far / dz, + 0, + ]; + testMat4WithAndWithoutDest((dst) => { + return mat4.frustumReverseZ(left, right, bottom, top, near, far, dst); + }, expected); + }); + + it('should compute correct frustumReverseZ', () => { + const left = -2; + const right = 4; + const top = 10; + const bottom = 30; + const near = 15; + const far = 25; + const m = mat4.frustumReverseZ(left, right, bottom, top, near, far); + shouldBeCloseArray(vec3.transformMat4([left, bottom, -near], m), [-1, -1, 1], 0.000001); + const centerX = (left + right) * 0.5; + const centerY = (top + bottom) * 0.5; + assertEqualApproximately(vec3.transformMat4([centerX, centerY, -near], m)[2], 1); + assertEqualApproximately(vec3.transformMat4([centerX, centerY, -far], m)[2], 0); + }); + it('should compute same frustum as perspective', () => { const lr = 4; const tb = 2;