text: /*************************************************************************/
  /*  triangulate.cpp                                                      */
  /*************************************************************************/
  /*                       This file is part of:                           */
  /*                           GODOT ENGINE                                */
  /*                    http://www.godotengine.org                         */
  /*************************************************************************/
  /* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
  /*                                                                       */
  /* Permission is hereby granted, free of charge, to any person obtaining */
  /* a copy of this software and associated documentation files (the       */
  /* "Software"), to deal in the Software without restriction, including   */
  /* without limitation the rights to use, copy, modify, merge, publish,   */
  /* distribute, sublicense, and/or sell copies of the Software, and to    */
  /* permit persons to whom the Software is furnished to do so, subject to */
  /* the following conditions:                                             */
  /*                                                                       */
  /* The above copyright notice and this permission notice shall be        */
  /* included in all copies or substantial portions of the Software.       */
  /*                                                                       */
  /* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,       */
  /* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF    */
  /* MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.*/
  /* IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY  */
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  /*************************************************************************/
  #include "triangulate.h"
  
  float Triangulate::get_area(const Vector<Vector2> &contour)
  {
  
    int n = contour.size();
    const Vector2 *c=&contour[0];
  
    float A=0.0f;
  
    for(int p=n-1,q=0; q<n; p=q++)
    {
      A+= c[p].cross(c[q]);
    }
    return A*0.5f;
  }
  
     /*
       is_inside_triangle decides if a point P is Inside of the triangle
       defined by A, B, C.
     */
  
  bool Triangulate::is_inside_triangle(float Ax, float Ay,
  		      float Bx, float By,
  		      float Cx, float Cy,
  		      float Px, float Py)
  
  {
    float ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
    float cCROSSap, bCROSScp, aCROSSbp;
  
    ax = Cx - Bx;  ay = Cy - By;
    bx = Ax - Cx;  by = Ay - Cy;
    cx = Bx - Ax;  cy = By - Ay;
    apx= Px - Ax;  apy= Py - Ay;
    bpx= Px - Bx;  bpy= Py - By;
    cpx= Px - Cx;  cpy= Py - Cy;
  
    aCROSSbp = ax*bpy - ay*bpx;
    cCROSSap = cx*apy - cy*apx;
    bCROSScp = bx*cpy - by*cpx;
  
    return ((aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f));
  };
  
  bool Triangulate::snip(const Vector<Vector2> &p_contour,int u,int v,int w,int n,const Vector<int>& V)
  {
    int p;
    float Ax, Ay, Bx, By, Cx, Cy, Px, Py;
    const Vector2 *contour=&p_contour[0];
  
    Ax = contour[V[u]].x;
    Ay = contour[V[u]].y;
  
    Bx = contour[V[v]].x;
    By = contour[V[v]].y;
  
    Cx = contour[V[w]].x;
    Cy = contour[V[w]].y;
  
    if ( CMP_EPSILON > (((Bx-Ax)*(Cy-Ay)) - ((By-Ay)*(Cx-Ax))) ) return false;
  
    for (p=0;p<n;p++)
    {
      if( (p == u) || (p == v) || (p == w) ) continue;
      Px = contour[V[p]].x;
      Py = contour[V[p]].y;
      if (is_inside_triangle(Ax,Ay,Bx,By,Cx,Cy,Px,Py)) return false;
    }
  
    return true;
  }
  
  bool Triangulate::triangulate(const Vector<Vector2> &contour,Vector<int> &result)
  {
    /* allocate and initialize list of Vertices in polygon */
  
    int n = contour.size();
    if ( n < 3 ) return false;
  
  
    Vector<int> V;
    V.resize(n);
  
    /* we want a counter-clockwise polygon in V */
  
    if ( 0.0f < get_area(contour) )
      for (int v=0; v<n; v++) V[v] = v;
    else
      for(int v=0; v<n; v++) V[v] = (n-1)-v;
  
    int nv = n;
  
    /*  remove nv-2 Vertices, creating 1 triangle every time */
    int count = 2*nv;   /* error detection */
  
    for(int v=nv-1; nv>2; )
    {
      /* if we loop, it is probably a non-simple polygon */
      if (0 >= (count--))
      {
        //** Triangulate: ERROR - probable bad polygon!
        return false;
      }
  
      /* three consecutive vertices in current polygon, <u,v,w> */
      int u = v  ; if (nv <= u) u = 0;     /* previous */
      v = u+1; if (nv <= v) v = 0;     /* new v    */
      int w = v+1; if (nv <= w) w = 0;     /* next     */
  
      if ( snip(contour,u,v,w,nv,V) )
      {
        int a,b,c,s,t;
  
        /* true names of the vertices */
        a = V[u]; b = V[v]; c = V[w];
  
        /* output Triangle */
        result.push_back( a );
        result.push_back( b );
        result.push_back( c );
  
        /* remove v from remaining polygon */
        for(s=v,t=v+1;t<nv;s++,t++)
  	    V[s] = V[t];
  
        nv--;
  
        /* resest error detection counter */
        count = 2*nv;
      }
    }
  
    return true;
  }
  