/*************************************************************************/ /* triangulate.cpp */ /*************************************************************************/ /* This file is part of: */ /* GODOT ENGINE */ /* http://www.godotengine.org */ /*************************************************************************/ /* Copyright (c) 2007-2015 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" 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,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; int *V = (int*)alloca(sizeof(int)*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 m=0, 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( contour[a] ); result.push_back( contour[b] ); result.push_back( contour[c] ); */ result.push_back( a ); result.push_back( b ); result.push_back( c ); m++; /* 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; }