//**********************************
//***      corners tools
// Written by Jarek Rossignac,  June 2006 
//**********************************
    
int t (int c) {int r=int(c/3); return(r);};
int n (int c) {int r=3*int(c/3)+(c+1)%3; return(r);};
int p (int c) {int r=3*int(c/3)+(c+2)%3; return(r);};
int v (int c) {return(V[c]);};
int o (int c) {return(O[c]);};
int l (int c) {return(o(n(c)));};
int r (int c) {return(o(p(c)));};
int w (int c) {return(W[c]);};               // temporary indices to mid-edge vertices associated with corners during subdivision
boolean border (int c) {return(O[c]==-1);};  // returns true if corner has no opposite
boolean nb(int c) {return(O[c]!=-1);};
pt g (int c) {return(G[V[c]]);};             // shortcut to get the point of the vertex v(c) of corner c

pt cg(int c) {pt cPt = midPt(g(c),midPt(g(c),triCenter(t(c))));  return(cPt); };   // computes point at corner
void showCorner(int c) {pt cPt = midPt(g(c),midPt(g(c),triCenter(t(c))));  cPt.show(3); };   // renders corner c as small ball
void drawEdge(int c) {line(g(p(c)).x,g(p(c)).y,g(p(c)).z,g(n(c)).x,g(n(c)).y,g(n(c)).z); };  // draws edge of t(c) opposite to corner c

void computeO() {                         // sets the O table from the V table, assumes consistent orientation of tirangles
  for (int i=0; i<3*nt; i++) {O[i]=-1;};  // init O table to -1: has no opposite (i.e. is a border corner)
  for (int i=0; i<3*nt; i++) {  for (int j=i+1; j<3*nt; j++) {       // for each corner i, for each other corner j
      if( (v(n(i))==v(p(j))) && (v(p(i))==v(n(j))) ) {O[i]=j; O[j]=i;};};}; // make i and j opposite if they match         
  };