text: /*************************************************************************
   *                                                                       *
   * Vega FEM Simulation Library Version 4.0                               *
   *                                                                       *
   * "mesher" library , Copyright (C) 2018 USC                             *
   * All rights reserved.                                                  *
   *                                                                       *
   * Code authors: Danyong Zhao, Yijing Li, Jernej Barbic                  *
   * http://www.jernejbarbic.com/vega                                      *
   *                                                                       *
   * Research: Jernej Barbic, Hongyi Xu, Yijing Li,                        *
   *           Danyong Zhao, Bohan Wang,                                   *
   *           Fun Shing Sin, Daniel Schroeder,                            *
   *           Doug L. James, Jovan Popovic                                *
   *                                                                       *
   * Funding: National Science Foundation, Link Foundation,                *
   *          Singapore-MIT GAMBIT Game Lab,                               *
   *          Zumberge Research and Innovation Fund at USC,                *
   *          Sloan Foundation, Okawa Foundation,                          *
   *          USC Annenberg Foundation                                     *
   *                                                                       *
   * This library is free software; you can redistribute it and/or         *
   * modify it under the terms of the BSD-style license that is            *
   * included with this library in the file LICENSE.txt                    *
   *                                                                       *
   * This library is distributed in the hope that it will be useful,       *
   * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
   * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the file     *
   * LICENSE.TXT for more details.                                         *
   *                                                                       *
   *************************************************************************/
  
  /*
    Intersection between a tet and a triangle.
  */
  
  #ifndef _TRIANGLETETINTERSECTION_H_
  #define _TRIANGLETETINTERSECTION_H_
  
  #include "vec3d.h"
  
  // This class computes whether a tetrahedron intersects a triangle, excluding just touching.
  class TriangleTetIntersection
  {
  public:
  
    // does the tetrahedron intersects the triangle, excluding just touching
    static bool tetrahedronIntersectTriangle(const Vec3d & tet1, const Vec3d & tet2, const Vec3d & tet3, const Vec3d & tet4, const Vec3d & t1, const Vec3d & t2, const Vec3d & t3);
  
  protected:
    class Tetrahedron
    {
    protected:
      // The positions of the four vertices
      const Vec3d v0, v1, v2, v3;
  
      // The normals of the four faces
      Vec3d n0, n1, n2, n3;
      // The positions of the four faces
      double d0, d1, d2, d3;
    public:
      Tetrahedron(const Vec3d & v0, const Vec3d & v1, const Vec3d & v2, const Vec3d & v3);
      // Whether a point is inside the tetrahedron, excluding on the tetrahedron
      bool contains(const Vec3d & p);
    };
  
    class Triangle 
    {
    protected:
      // The positions of the three vertices
      const Vec3d v0, v1, v2;
      // The normal
      Vec3d n;
      // The position of the face
      double d;
      // The two base vectors of the face
      Vec3d base1, base2;
    public:
      Triangle(const Vec3d & v0, const Vec3d & v1, const Vec3d & v2);
      // Whether a point is inside the triangle, excluding on the triangle
      bool contains(const Vec3d & p);
      // Whether the segment starting from l0 and ending at l1 intersects the triangle, excluding just touching
      bool intersect(const Vec3d & l0, const Vec3d & l1);
    };
  
    //compute the determinant of a 3x3 matrix defined by three vectors whose dimensions are all three
    static inline double det(const Vec3d & a, const Vec3d & b, const Vec3d & c) { return dot(a, cross(b, c)); }
  
  private:
    TriangleTetIntersection();
  };
  
  #endif /* INTERSECTION_H_ */
  
  