tri.h

/*
 * Copyright (C) 2015, Nils Moehrle
 * TU Darmstadt - Graphics, Capture and Massively Parallel Computing
 * All rights reserved.
 *
 * This software may be modified and distributed under the terms
 * of the BSD 3-Clause license. See the LICENSE.txt file for details.
 */

#ifndef TEX_TRI_HEADER
#define TEX_TRI_HEADER

#include "math/vector.h"
#include "math/matrix.h"
#include "rect.h"

/**
  * Simple class representing a two dimensional triangle optimized for the calculation of barycentric coordinates.
  */
class Tri {
    private:
        math::Vec2f v1;
        math::Vec2f v2;
        math::Vec2f v3;
        float detT;

        Rect<float> aabb;
    public:
        /** Constructor which calculates the axis aligned bounding box and prepares the calculation of barycentric coordinates. */
        Tri(math::Vec2f v1, math::Vec2f v2, math::Vec2f v3);

        /** Determines whether the given point is inside via barycentric coordinates. */
        bool inside(float x, float y) const;

        /** Returns the barycentric coordinates for the given point. */
        math::Vec3f get_barycentric_coords(float x, float y) const;

        /** Returns the area of the triangle. */
        float get_area(void) const;

        /** Returns the axis aligned bounding box. */
        Rect<float> get_aabb(void) const;
};

inline Rect<float>
Tri::get_aabb(void) const {
    return aabb;
}

inline math::Vec3f
Tri::get_barycentric_coords(float x, float y) const {
    float const alpha = ((v2[1] - v3[1]) * (x - v3[0]) + (v3[0] - v2[0]) * (y - v3[1])) / detT;
    float const beta = ((v3[1] - v1[1]) * (x - v3[0]) + (v1[0] - v3[0]) * (y - v3[1])) / detT;
    float const gamma = 1.0f - alpha - beta;
    return math::Vec3f(alpha, beta, gamma);
}

inline bool
Tri::inside(float x, float y) const {
    float const dx = (x - v3[0]);
    float const dy = (y - v3[1]);

    float const alpha = ((v2[1] - v3[1]) * dx + (v3[0] - v2[0]) * dy) / detT;
    if (alpha < 0.0f || alpha > 1.0f)
        return false;

    float const beta = ((v3[1] - v1[1]) * dx + (v1[0] - v3[0]) * dy) / detT;
    if (beta < 0.0f || beta > 1.0f)
        return false;

    if (alpha + beta > 1.0f)
        return false;

    /* else */
    return true;
}

inline float
Tri::get_area(void) const {
    math::Vec2f u = v2 - v1;
    math::Vec2f v = v3 - v1;

    return 0.5f * std::abs(u[0] * v[1] - u[1] * v[0]);
}

#endif /* TEX_TRI_HEADER */