triangulate.cpp
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00001 #include <stdio.h>
00002 #include <stdlib.h>
00003 #include <string.h>
00004 #include <assert.h>
00005 #include <math.h>
00006 
00063 #include <vector>  // Include STL vector class.
00064 
00065 #include "triangulate.h"
00066 
00067 
00068 namespace ConvexDecomposition
00069 {
00070 
00071 
00072 class Vec2d
00073 {
00074 public:
00075         Vec2d(const double *v)
00076         {
00077                 mX = v[0];
00078                 mY = v[1];
00079         }
00080   Vec2d(double x,double y)
00081   {
00082     Set(x,y);
00083   };
00084   double GetX(void) const { return mX; };
00085   double GetY(void) const { return mY; };
00086 
00087   void  Set(double x,double y)
00088   {
00089     mX = x;
00090     mY = y;
00091   };
00092 
00093 private:
00094   double mX;
00095   double mY;
00096 };// Typedef an STL vector of vertices which are used to represent
00097 // a polygon/contour and a series of triangles.
00098 
00099 typedef std::vector< Vec2d > Vec2dVector;
00100 
00101 static bool Process(const Vec2dVector &contour,Vec2dVector &result);  // compute area of a contour/polygon
00102 static double Area(const Vec2dVector &contour);  // decide if point Px/Py is inside triangle defined by (Ax,Ay) (Bx,By) (Cx,Cy)
00103 static bool InsideTriangle(double Ax, double Ay,double Bx, double By,double Cx, double Cy,double Px, double Py);
00104 static bool Snip(const Vec2dVector &contour,int u,int v,int w,int n,int *V);
00105 
00106 static const double EPSILON=0.0000000001f;
00107 
00108 double Area(const Vec2dVector &contour)
00109 {
00110   int n = contour.size();
00111   double A=0.0f;
00112   for(int p=n-1,q=0; q<n; p=q++)
00113   {
00114     A+= contour[p].GetX()*contour[q].GetY() - contour[q].GetX()*contour[p].GetY();
00115   }
00116   return A*0.5f;
00117 }
00118 /*
00119   InsideTriangle decides if a point P is Inside of the triangle
00120   defined by A, B, C.
00121 */
00122 bool InsideTriangle(double Ax, double Ay,double Bx, double By,double Cx, double Cy,double Px, double Py)
00123 {
00124   double ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
00125   double cCROSSap, bCROSScp, aCROSSbp;  ax = Cx - Bx;  ay = Cy - By;
00126   bx = Ax - Cx;  by = Ay - Cy;
00127   cx = Bx - Ax;  cy = By - Ay;
00128   apx= Px - Ax;  apy= Py - Ay;
00129   bpx= Px - Bx;  bpy= Py - By;
00130   cpx= Px - Cx;  cpy= Py - Cy;  aCROSSbp = ax*bpy - ay*bpx;
00131   cCROSSap = cx*apy - cy*apx;
00132   bCROSScp = bx*cpy - by*cpx;  return ((aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f));
00133 };
00134 
00135 bool Snip(const Vec2dVector &contour,int u,int v,int w,int n,int *V)
00136 {
00137   int p;
00138   double Ax, Ay, Bx, By, Cx, Cy, Px, Py;
00139   Ax = contour[V[u]].GetX();
00140   Ay = contour[V[u]].GetY();
00141   Bx = contour[V[v]].GetX();
00142   By = contour[V[v]].GetY();
00143   Cx = contour[V[w]].GetX();
00144   Cy = contour[V[w]].GetY();
00145   if ( EPSILON > (((Bx-Ax)*(Cy-Ay)) - ((By-Ay)*(Cx-Ax))) ) return false;  for (p=0;p<n;p++)
00146   {
00147     if( (p == u) || (p == v) || (p == w) ) continue;
00148     Px = contour[V[p]].GetX();
00149     Py = contour[V[p]].GetY();
00150     if (InsideTriangle(Ax,Ay,Bx,By,Cx,Cy,Px,Py)) return false;
00151   }  return true;
00152 }
00153 
00154 bool Process(const Vec2dVector &contour,Vec2dVector &result)
00155 {
00156   /* allocate and initialize list of Vertices in polygon */
00157   int n = contour.size();
00158   if ( n < 3 ) return false;  int *V = new int[n];  /* we want a counter-clockwise polygon in V */  if ( 0.0f < Area(contour) )
00159     for (int v=0; v<n; v++) V[v] = v;
00160   else
00161     for(int v=0; v<n; v++) V[v] = (n-1)-v;  int nv = n;  /*  remove nv-2 Vertices, creating 1 triangle every time */
00162 
00163   int count = 2*nv;   /* error detection */
00164 
00165   for(int m=0, v=nv-1; nv>2; )
00166   {
00167     /* if we loop, it is probably a non-simple polygon */
00168     if (0 >= (count--))
00169     {
00170       //** Triangulate: ERROR - probable bad polygon!
00171       return false;
00172     }    /* three consecutive vertices in current polygon, <u,v,w> */
00173 
00174     int u = v  ; 
00175                 if (nv <= u) u = 0;     /* previous */
00176     v = u+1; if (nv <= v) v = 0;     /* new v    */
00177     int w = v+1;
00178     if (nv <= w) w = 0;     /* next     */
00179 
00180     if ( Snip(contour,u,v,w,nv,V) )
00181     {
00182       int a,b,c,s,t;      /* true names of the vertices */
00183 
00184       a = V[u]; 
00185                         b = V[v];
00186                         c = V[w];      /* output Triangle */
00187 
00188       result.push_back( contour[a] );
00189       result.push_back( contour[b] );
00190       result.push_back( contour[c] );
00191 
00192       m++;      /* remove v from remaining polygon */
00193       for(s=v,t=v+1;t<nv;s++,t++) V[s] = V[t]; nv--;      /* resest error detection counter */
00194       count = 2*nv;
00195     }
00196 
00197   }
00198   delete V;
00199   return true;
00200 }
00201 
00202 
00203 unsigned int triangulate3d(unsigned int pcount,     // number of points in the polygon
00204                            const double *vertices,   // array of 3d vertices.
00205                            double *triangles,        // memory to store output triangles
00206                            unsigned int maxTri,    // maximum triangles we are allowed to output.
00207                            const double *plane)
00208 
00209 {
00210   unsigned int ret = 0;
00211 
00212   FILE *fph = fopen("debug.obj", "wb");
00213   if ( fph )
00214   {
00215     fprintf(fph,"v 10 10 0\r\n");
00216     for (unsigned int i=0; i<pcount; i++)
00217     {
00218       fprintf(fph,"v %f %f %f\r\n", vertices[i*3+0], vertices[i*3+1], vertices[i*3+2]);
00219     }
00220     for (unsigned int i=0; i<pcount; i++)
00221     {
00222       unsigned int next = i+1;
00223       if ( next == pcount ) next = 0;
00224       fprintf(fph,"f %d %d %d\r\n", i+2, 1, next+2 );
00225     }
00226     fclose(fph);
00227   }
00228 
00229   if ( pcount >= 3 )
00230   {
00231     double normal[3];
00232 
00233     normal[0] = plane[0];
00234     normal[1] = plane[1];
00235     normal[2] = plane[2];
00236     double D = plane[3];
00237 
00238     unsigned int i0 = 0;
00239     unsigned int i1 = 1;
00240     unsigned int i2 = 2;
00241     unsigned int axis = 0;
00242 
00243 
00244     // find the dominant axis.
00245     double dx = fabs(normal[0]);
00246     double dy = fabs(normal[1]);
00247     double dz = fabs(normal[2]);
00248 
00249     if ( dx > dy && dx > dz )
00250     {
00251       axis = 0;
00252       i0   = 1;
00253       i1   = 2;
00254       i2   = 0;
00255     }
00256     else if ( dy > dx && dy > dz )
00257     {
00258       i0   = 0;
00259       i1   = 2;
00260       i2   = 1;
00261       axis = 1;
00262     }
00263     else if ( dz > dx && dz > dy )
00264     {
00265       i0 = 0;
00266       i1 = 1;
00267       i2 = 2;
00268       axis = 2;
00269     }
00270 
00271     double *ptemp = new double[pcount*2];
00272     double *ptri  = new double[maxTri*2*3];
00273     const double *source = vertices;
00274     double *dest = ptemp;
00275 
00276     for (unsigned int i=0; i<pcount; i++)
00277     {
00278 
00279       dest[0] = source[i0];
00280       dest[1] = source[i1];
00281 
00282       dest+=2;
00283       source+=3;
00284     }
00285 
00286     ret = triangulate2d(pcount, ptemp, ptri, maxTri );
00287 
00288     // ok..now we have to copy it back and project the 3d component.
00289     if ( ret )
00290     {
00291       const double *source = ptri;
00292       double *dest = triangles;
00293 
00294                         double inverseZ = -1.0f / normal[i2];
00295 
00296       for (unsigned int i=0; i<ret*3; i++)
00297       {
00298 
00299         dest[i0] = source[0];
00300         dest[i1] = source[1];
00301 
00302         dest[i2] = (normal[i0]*source[0] + normal[i1]*source[1] + D ) * inverseZ; // solve for projected component
00303 
00304         dest+=3;
00305         source+=2;
00306       }
00307 
00308 
00309      if ( 1 )
00310      {
00311       FILE *fph = fopen("test.obj","wb");
00312       const double *source = triangles;
00313       for (unsigned int i=0; i<ret*3; i++)
00314       {
00315         fprintf(fph,"v %f %f %f\r\n", source[0], source[1], source[2] );
00316         source+=3;
00317       }
00318       int index = 1;
00319       for (unsigned int i=0; i<ret; i++)
00320       {
00321         fprintf(fph,"f %d %d %d\r\n", index, index+1, index+2 );
00322         index+=3;
00323       }
00324       fclose(fph);
00325                 }
00326                 }
00327 
00328     delete ptri;
00329     delete ptemp;
00330 
00331   }
00332 
00333   return ret;
00334 }
00335 
00336 unsigned int triangulate3d(unsigned int pcount,     // number of points in the polygon
00337                            const unsigned int *indices, // polygon points using indices
00338                            const double *vertices,   // base address for array indexing
00339                            double *triangles,        // buffer to store output 3d triangles.
00340                            unsigned int maxTri,    // maximum triangles we can output.
00341                            const double *plane)
00342 {
00343   unsigned int ret = 0;
00344 
00345   if ( pcount )
00346   {
00347     // copy the indexed polygon out as a flat array of vertices.
00348     double *ptemp = new double[pcount*3];
00349     double *dest = ptemp;
00350 
00351     for (unsigned int i=0; i<pcount; i++)
00352     {
00353       unsigned int index = indices[i];
00354       const double *source = &vertices[index*3];
00355       *dest++ = *source++;
00356       *dest++ = *source++;
00357       *dest++ = *source++;
00358     }
00359 
00360     ret = triangulate3d(pcount,ptemp,triangles,maxTri,plane);
00361 
00362     delete ptemp;
00363   }
00364 
00365   return ret;
00366 }
00367 
00368 unsigned int triangulate2d(unsigned int pcount,     // number of points in the polygon
00369                            const double *vertices,   // address of input points (2d)
00370                            double *triangles,        // destination buffer for output triangles.
00371                            unsigned int maxTri)    // maximum number of triangles we can store.
00372 {
00373   unsigned int ret = 0;
00374 
00375   const double *source = vertices;
00376   Vec2dVector vlist;
00377 
00378   for (unsigned int i=0; i<pcount; i++)
00379   {
00380     Vec2d v(source);
00381     vlist.push_back(v);
00382     source+=2;
00383   }
00384 
00385   Vec2dVector result;
00386 
00387   bool ok = Process(vlist,result);
00388   if ( ok )
00389   {
00390     ret = result.size()/3;
00391     if ( ret < maxTri )
00392     {
00393       double *dest = triangles;
00394       for (unsigned int i=0; i<ret*3; i++)
00395       {
00396         dest[0] = result[i].GetX();
00397         dest[1] = result[i].GetY();
00398         dest+=2;
00399       }
00400     }
00401     else
00402     {
00403       ret = 0;
00404     }
00405   }
00406 
00407   return ret;
00408 }
00409 
00410 }; // end of namespace
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convex_decomposition
Author(s): John Ratcliff
autogenerated on Mon Aug 19 2013 11:02:33