godot/core/math/triangulate.cpp

/*************************************************************************/
/*  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  */
/* CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,  */
/* TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE     */
/* SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                */
/*************************************************************************/
#include "triangulate.h"

real_t Triangulate::get_area(const Vector<Vector2> &contour)
{

  int n = contour.size();
  const Vector2 *c=&contour[0];

  real_t A=0.0;

  for(int p=n-1,q=0; q<n; p=q++)
  {
    A+= c[p].cross(c[q]);
  }
  return A*0.5;
}

   /*
     is_inside_triangle decides if a point P is Inside of the triangle
     defined by A, B, C.
   */

bool Triangulate::is_inside_triangle(real_t Ax, real_t Ay,
		      real_t Bx, real_t By,
		      real_t Cx, real_t Cy,
		      real_t Px, real_t Py)

{
  real_t ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
  real_t 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 >= 0.0) && (bCROSScp >= 0.0) && (cCROSSap >= 0.0));
};

bool Triangulate::snip(const Vector<Vector2> &p_contour,int u,int v,int w,int n,const Vector<int>& V)
{
  int p;
  real_t 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 ( 0.0 < 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;
}