text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkTriangle.h
  
    Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
    All rights reserved.
    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
  
       This software is distributed WITHOUT ANY WARRANTY; without even
       the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
       PURPOSE.  See the above copyright notice for more information.
  
  =========================================================================*/
  /**
   * @class   vtkTriangle
   * @brief   a cell that represents a triangle
   *
   * vtkTriangle is a concrete implementation of vtkCell to represent a triangle
   * located in 3-space.
  */
  
  #ifndef vtkTriangle_h
  #define vtkTriangle_h
  
  #include "vtkCommonDataModelModule.h" // For export macro
  #include "vtkCell.h"
  
  #include "vtkMath.h" // Needed for inline methods
  
  class vtkLine;
  class vtkQuadric;
  class vtkIncrementalPointLocator;
  
  class VTKCOMMONDATAMODEL_EXPORT vtkTriangle : public vtkCell
  {
  public:
    static vtkTriangle *New();
    vtkTypeMacro(vtkTriangle,vtkCell);
    void PrintSelf(ostream& os, vtkIndent indent) override;
  
    /**
     * Get the edge specified by edgeId (range 0 to 2) and return that edge's
     * coordinates.
     */
    vtkCell *GetEdge(int edgeId) override;
  
    //@{
    /**
     * See the vtkCell API for descriptions of these methods.
     */
    int GetCellType() override {return VTK_TRIANGLE;};
    int GetCellDimension() override {return 2;};
    int GetNumberOfEdges() override {return 3;};
    int GetNumberOfFaces() override {return 0;};
    vtkCell *GetFace(int) override {return nullptr;};
    int CellBoundary(int subId, double pcoords[3], vtkIdList *pts) override;
    void Contour(double value, vtkDataArray *cellScalars,
                 vtkIncrementalPointLocator *locator, vtkCellArray *verts,
                 vtkCellArray *lines, vtkCellArray *polys,
                 vtkPointData *inPd, vtkPointData *outPd,
                 vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd) override;
    int EvaluatePosition(double x[3], double* closestPoint,
                         int& subId, double pcoords[3],
                         double& dist2, double *weights) override;
    void EvaluateLocation(int& subId, double pcoords[3], double x[3],
                          double *weights) override;
    int Triangulate(int index, vtkIdList *ptIds, vtkPoints *pts) override;
    void Derivatives(int subId, double pcoords[3], double *values,
                     int dim, double *derivs) override;
    double *GetParametricCoords() override;
    //@}
  
    /**
     * A convenience function to compute the area of a vtkTriangle.
     */
    double ComputeArea();
  
    /**
     * Clip this triangle using scalar value provided. Like contouring, except
     * that it cuts the triangle to produce other triangles.
     */
    void Clip(double value, vtkDataArray *cellScalars,
              vtkIncrementalPointLocator *locator, vtkCellArray *polys,
              vtkPointData *inPd, vtkPointData *outPd,
              vtkCellData *inCd, vtkIdType cellId, vtkCellData *outCd,
              int insideOut) override;
  
    /**
     * @deprecated Replaced by vtkTriangle::InterpolateFunctions as of VTK 5.2
     */
    static void InterpolationFunctions(double pcoords[3], double sf[3]);
    /**
     * @deprecated Replaced by vtkTriangle::InterpolateDerivs as of VTK 5.2
     */
    static void InterpolationDerivs(double pcoords[3], double derivs[6]);
    //@{
    /**
     * Compute the interpolation functions/derivatives
     * (aka shape functions/derivatives)
     */
    void InterpolateFunctions(double pcoords[3], double sf[3]) override
    {
      vtkTriangle::InterpolationFunctions(pcoords,sf);
    }
    void InterpolateDerivs(double pcoords[3], double derivs[6]) override
    {
      vtkTriangle::InterpolationDerivs(pcoords,derivs);
    }
    //@}
    /**
     * Return the ids of the vertices defining edge (`edgeId`).
     * Ids are related to the cell, not to the dataset.
     */
    int *GetEdgeArray(int edgeId);
  
    /**
     * Plane intersection plus in/out test on triangle. The in/out test is
     * performed using tol as the tolerance.
     */
    int IntersectWithLine(double p1[3], double p2[3], double tol, double& t,
                          double x[3], double pcoords[3], int& subId) override;
  
    /**
     * Return the center of the triangle in parametric coordinates.
     */
    int GetParametricCenter(double pcoords[3]) override;
  
    /**
     * Return the distance of the parametric coordinate provided to the
     * cell. If inside the cell, a distance of zero is returned.
     */
    double GetParametricDistance(double pcoords[3]) override;
  
    /**
     * Compute the center of the triangle.
     */
    static void TriangleCenter(double p1[3], double p2[3], double p3[3],
                               double center[3]);
  
    /**
     * Compute the area of a triangle in 3D.
     * See also vtkTriangle::ComputeArea()
     */
    static double TriangleArea(double p1[3], double p2[3], double p3[3]);
  
    /**
     * Compute the circumcenter (center[3]) and radius squared (method
     * return value) of a triangle defined by the three points x1, x2,
     * and x3. (Note that the coordinates are 2D. 3D points can be used
     * but the z-component will be ignored.)
     */
    static double Circumcircle(double  p1[2], double p2[2], double p3[2],
                              double center[2]);
  
    /**
     * Given a 2D point x[2], determine the barycentric coordinates of the point.
     * Barycentric coordinates are a natural coordinate system for simplices that
     * express a position as a linear combination of the vertices. For a
     * triangle, there are three barycentric coordinates (because there are
     * three vertices), and the sum of the coordinates must equal 1. If a
     * point x is inside a simplex, then all three coordinates will be strictly
     * positive.  If two coordinates are zero (so the third =1), then the
     * point x is on a vertex. If one coordinates are zero, the point x is on an
     * edge. In this method, you must specify the vertex coordinates x1->x3.
     * Returns 0 if triangle is degenerate.
     */
    static int BarycentricCoords(double x[2], double  x1[2], double x2[2],
                                 double x3[2], double bcoords[3]);
  
  
    /**
     * Project triangle defined in 3D to 2D coordinates. Returns 0 if
     * degenerate triangle; non-zero value otherwise. Input points are x1->x3;
     * output 2D points are v1->v3.
     */
    static int ProjectTo2D(double x1[3], double x2[3], double x3[3],
                           double v1[2], double v2[2], double v3[2]);
  
    /**
     * Compute the triangle normal from a points list, and a list of point ids
     * that index into the points list.
     */
    static void ComputeNormal(vtkPoints *p, int numPts, vtkIdType *pts,
                              double n[3]);
  
    /**
     * Compute the triangle normal from three points.
     */
    static void ComputeNormal(double v1[3], double v2[3], double v3[3], double n[3]);
  
    /**
     * Compute the (unnormalized) triangle normal direction from three points.
     */
    static void ComputeNormalDirection(double v1[3], double v2[3], double v3[3],
                                       double n[3]);
  
    // Description:
    // Determine whether or not triangle (p1,q1,r1) intersects triangle
    // (p2,q2,r2). This method is adapted from Olivier Devillers, Philippe Guigue.
    // Faster Triangle-Triangle Intersection Tests. RR-4488, IN-RIA. 2002.
    // <inria-00072100>.
    static int TrianglesIntersect(double p1[3], double q1[3], double r1[3],
                                  double p2[3], double q2[3], double r2[3]);
  
    // Description:
    // Given a point x, determine whether it is inside (within the
    // tolerance squared, tol2) the triangle defined by the three
    // coordinate values p1, p2, p3. Method is via comparing dot products.
    // (Note: in current implementation the tolerance only works in the
    // neighborhood of the three vertices of the triangle.
    static int PointInTriangle(double x[3], double x1[3],
                               double x2[3], double x3[3],
                               double tol2);
  
    //@{
    /**
     * Calculate the error quadric for this triangle.  Return the
     * quadric as a 4x4 matrix or a vtkQuadric.  (from Peter
     * Lindstrom's Siggraph 2000 paper, "Out-of-Core Simplification of
     * Large Polygonal Models")
     */
    static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
                               double quadric[4][4]);
    static void ComputeQuadric(double x1[3], double x2[3], double x3[3],
                               vtkQuadric *quadric);
    //@}
  
  
  protected:
    vtkTriangle();
    ~vtkTriangle() override;
  
    vtkLine *Line;
  
  private:
    vtkTriangle(const vtkTriangle&) = delete;
    void operator=(const vtkTriangle&) = delete;
  };
  
  //----------------------------------------------------------------------------
  inline int vtkTriangle::GetParametricCenter(double pcoords[3])
  {
    pcoords[0] = pcoords[1] = 1./3; pcoords[2] = 0.0;
    return 0;
  }
  
  //----------------------------------------------------------------------------
  inline void vtkTriangle::ComputeNormalDirection(double v1[3], double v2[3],
                                         double v3[3], double n[3])
  {
    double ax, ay, az, bx, by, bz;
  
    // order is important!!! maintain consistency with triangle vertex order
    ax = v3[0] - v2[0]; ay = v3[1] - v2[1]; az = v3[2] - v2[2];
    bx = v1[0] - v2[0]; by = v1[1] - v2[1]; bz = v1[2] - v2[2];
  
    n[0] = (ay * bz - az * by);
    n[1] = (az * bx - ax * bz);
    n[2] = (ax * by - ay * bx);
  }
  
  //----------------------------------------------------------------------------
  inline void vtkTriangle::ComputeNormal(double v1[3], double v2[3],
                                         double v3[3], double n[3])
  {
    double length;
  
    vtkTriangle::ComputeNormalDirection(v1, v2, v3, n);
  
    if ( (length = sqrt((n[0]*n[0] + n[1]*n[1] + n[2]*n[2]))) != 0.0 )
    {
      n[0] /= length;
      n[1] /= length;
      n[2] /= length;
    }
  }
  
  //----------------------------------------------------------------------------
  inline void vtkTriangle::TriangleCenter(double p1[3], double p2[3],
                                          double p3[3], double center[3])
  {
    center[0] = (p1[0]+p2[0]+p3[0]) / 3.0;
    center[1] = (p1[1]+p2[1]+p3[1]) / 3.0;
    center[2] = (p1[2]+p2[2]+p3[2]) / 3.0;
  }
  
  //----------------------------------------------------------------------------
  inline double vtkTriangle::TriangleArea(double p1[3], double p2[3], double p3[3])
  {
    double n[3];
    vtkTriangle::ComputeNormalDirection(p1,p2,p3,n);
  
    return 0.5*vtkMath::Norm(n);
  }
  
  #endif
  