// cube.cpp // by Glenn G. Chappell and Chris Hartman // Begin: 16 May 2001 // Current: 22 Feb 2002 #include "cube.h" #include #include #include #include using std::sort; // bitsout() // ???xxxx -> x00x00x00x // Number of bits (x's) = DEPTH template int Cube::bitsout(int in) { int out = 0; for (int ii=0,inmask=1,outmask=1; ii xxxx // Number of bits (x's) = DEPTH template int Cube::bitsin(int out) { int in = 0; for (int ii=0,inmask=1,outmask=1; ii Cube::Cube(Potentialtype startthresh, // =0 Potentialtype startpot, // =0 Vertcoordtype bigcubewidth, // =1 Vertcoordtype originx, // =0 Vertcoordtype originy, // =0 Vertcoordtype originz) // =0 :threshold(startthresh) { cubiewidth = bigcubewidth/(POTSIDE-1); origin[0] = originx; origin[1] = originy; origin[2] = originz; modifiedleaves.reserve(CUBIES); // CUBIES = number of leaf nodes modifiedinternals.reserve(FIRSTLEAF); // FIRSTLEAF = number of internal nodes for (int n=0; n>1); vertsubstable[cubien][2] = bitsin(ii>>2); leafmodified[cubien] = false; } } template void Cube::surfspit(void (* handletri)(Triangle &)) { if(!modifiedleaves.empty()) update(); ssrecurse(0,handletri); } template void Cube::ssrecurse(int n, void (* handletri)(Triangle &)) { if (data[n].minv < threshold && data[n].maxv >= threshold) { if(isleaf(n)) { vector_Triangle::iterator jj; vector_Triangle & mytris = data[n].ld.tris; for(jj=mytris.begin(); jj!=mytris.end(); ++jj) handletri(*jj); } else for(int ii=1;ii<=8;++ii) ssrecurse(8*n+ii,handletri); } } template void Cube::update() //set maxv-minv's from bottom up { vector_int::iterator iter; assert(modifiedinternals.empty()); if(modifiedleaves.empty()) return; sort(modifiedleaves.begin(),modifiedleaves.end()); // cubies must be re-calc'd in lo-to-hi order int lastputon = -1; //nonexistent value - nothing was put on most recently for (iter=modifiedleaves.begin(); iter!=modifiedleaves.end(); ++iter) { int curnode = *iter; leafmodified[curnode] = false; recalccubie(curnode); int parent = (curnode-1)/8; if(parent != lastputon) { modifiedinternals.push_back(parent); lastputon = parent; } } modifiedleaves.erase(modifiedleaves.begin(),modifiedleaves.end()); for (iter=modifiedinternals.begin(); iter!=modifiedinternals.end(); ++iter) // Note: end() changes, but we have reserved space, so iterator remains valid. { int curnode = *iter; int childbase = curnode*8+1; Potentialtype maxval = data[childbase].maxv; Potentialtype minval = data[childbase].minv; for (int jj=1; jj<=7; ++jj) { if (data[childbase+jj].maxv > maxval) maxval = data[childbase+jj].maxv; if (data[childbase+jj].minv < minval) minval = data[childbase+jj].minv; } data[curnode].maxv = maxval; data[curnode].minv = minval; int parent = (curnode-1)/8; if((curnode != 0) && parent != lastputon) { modifiedinternals.push_back(parent); lastputon = parent; } } modifiedinternals.erase(modifiedinternals.begin(),modifiedinternals.end()); } template void Cube::setthreshold(Potentialtype t) { if(!modifiedleaves.empty()) update(); Potentialtype oldt=threshold; threshold=t; stdowndate(oldt,0); } template void Cube::stdowndate(Potentialtype oldt, int n) { if( (data[n].minv=oldt) || (data[n].minv=threshold)) { if(isleaf(n)) recalccubie(n); // cubies must be re-calc'd in lo-to-hi order else for(int ii=1;ii<=8;++ii) stdowndate(oldt,8*n+ii); } } template inline void Cube::markleafasmodified(int xsub, int ysub, int zsub) { int n = nodenumtable[xsub][ysub][zsub]; if (!leafmodified[n]) { modifiedleaves.push_back(n); leafmodified[n] = true; } } template void Cube::setpotential(int xsub, int ysub, int zsub, Potentialtype newpot) { if (xsub<0 || xsub>=POTSIDE || ysub<0 || ysub>=POTSIDE || zsub<0 || zsub>=POTSIDE) return; potentials[xsub][ysub][zsub] = newpot; switch( (xsub==0) + ((xsub==POTSIDE-1)<<1) + ((ysub==0)<<2) + ((ysub==POTSIDE-1)<<3) + ((zsub==0)<<4) + ((zsub==POTSIDE-1)<<5)) { case 0: // (000 base 4) boundaries: x -- y -- z -- markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub-1,ysub ,zsub ); markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub-1,zsub ); markleafasmodified(xsub ,ysub ,zsub-1); markleafasmodified(xsub ,ysub ,zsub ); break; case 1: // (001 base 4) boundaries: x lo y -- z -- markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub-1,zsub ); markleafasmodified(xsub ,ysub ,zsub-1); markleafasmodified(xsub ,ysub ,zsub ); break; case 2: // (002 base 4) boundaries: x HI y -- z -- markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub-1,ysub ,zsub ); break; case 4: // (010 base 4) boundaries: x -- y lo z -- markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub-1,ysub ,zsub ); markleafasmodified(xsub ,ysub ,zsub-1); markleafasmodified(xsub ,ysub ,zsub ); break; case 5: // (011 base 4) boundaries: x lo y lo z -- markleafasmodified(xsub ,ysub ,zsub-1); markleafasmodified(xsub ,ysub ,zsub ); break; case 6: // (012 base 4) boundaries: x HI y lo z -- markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub-1,ysub ,zsub ); break; case 8: // (020 base 4) boundaries: x -- y HI z -- markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub-1,zsub ); break; case 9: // (021 base 4) boundaries: x lo y HI z -- markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub-1,zsub ); break; case 10: // (022 base 4) boundaries: x HI y HI z -- markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub-1,zsub ); break; case 16: // (100 base 4) boundaries: x -- y -- z lo markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub-1,ysub ,zsub ); markleafasmodified(xsub ,ysub-1,zsub ); markleafasmodified(xsub ,ysub ,zsub ); break; case 17: // (101 base 4) boundaries: x lo y -- z lo markleafasmodified(xsub ,ysub-1,zsub ); markleafasmodified(xsub ,ysub ,zsub ); break; case 18: // (102 base 4) boundaries: x HI y -- z lo markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub-1,ysub ,zsub ); break; case 20: // (110 base 4) boundaries: x -- y lo z lo markleafasmodified(xsub-1,ysub ,zsub ); markleafasmodified(xsub ,ysub ,zsub ); break; case 21: // (111 base 4) boundaries: x lo y lo z lo markleafasmodified(xsub ,ysub ,zsub ); break; case 22: // (112 base 4) boundaries: x HI y lo z lo markleafasmodified(xsub-1,ysub ,zsub ); break; case 24: // (120 base 4) boundaries: x -- y HI z lo markleafasmodified(xsub-1,ysub-1,zsub ); markleafasmodified(xsub ,ysub-1,zsub ); break; case 25: // (121 base 4) boundaries: x lo y HI z lo markleafasmodified(xsub ,ysub-1,zsub ); break; case 26: // (122 base 4) boundaries: x HI y HI z lo markleafasmodified(xsub-1,ysub-1,zsub ); break; case 32: // (200 base 4) boundaries: x -- y -- z HI markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub ,zsub-1); break; case 33: // (201 base 4) boundaries: x lo y -- z HI markleafasmodified(xsub ,ysub-1,zsub-1); markleafasmodified(xsub ,ysub ,zsub-1); break; case 34: // (202 base 4) boundaries: x HI y -- z HI markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub-1,ysub ,zsub-1); break; case 36: // (210 base 4) boundaries: x -- y lo z HI markleafasmodified(xsub-1,ysub ,zsub-1); markleafasmodified(xsub ,ysub ,zsub-1); break; case 37: // (211 base 4) boundaries: x lo y lo z HI markleafasmodified(xsub ,ysub ,zsub-1); break; case 38: // (212 base 4) boundaries: x HI y lo z HI markleafasmodified(xsub-1,ysub ,zsub-1); break; case 40: // (220 base 4) boundaries: x -- y HI z HI markleafasmodified(xsub-1,ysub-1,zsub-1); markleafasmodified(xsub ,ysub-1,zsub-1); break; case 41: // (221 base 4) boundaries: x lo y HI z HI markleafasmodified(xsub ,ysub-1,zsub-1); break; case 42: // (222 base 4) boundaries: x HI y HI z HI markleafasmodified(xsub-1,ysub-1,zsub-1); break; default: assert(0); } } // calcXintersection // Calculate vertex & normal coords for vertex on an edge in the x direction. // Parameters are x,y,z subscripts of low end of edge -- // same as subscripts of edge in xeverts array. template inline void Cube::calcXintersection(int xs, int ys, int zs) { int xsm1 = (xs==0) ? xs : xs-1; int xsp2 = (xs==POTSIDE-2) ? xs+1 : xs+2; int ysm1 = (ys==0) ? ys : ys-1; int ysp1 = (ys==POTSIDE-1) ? ys : ys+1; int zsm1 = (zs==0) ? zs : zs-1; int zsp1 = (zs==POTSIDE-1) ? zs : zs+1; Potentialtype p011 = potentials[xsm1][ys ][zs ]; Potentialtype p111 = potentials[xs ][ys ][zs ]; Potentialtype p211 = potentials[xs+1][ys ][zs ]; Potentialtype p311 = potentials[xsp2][ys ][zs ]; Potentialtype p101 = potentials[xs ][ysm1][zs ]; Potentialtype p121 = potentials[xs ][ysp1][zs ]; Potentialtype p110 = potentials[xs ][ys ][zsm1]; Potentialtype p112 = potentials[xs ][ys ][zsp1]; Potentialtype p201 = potentials[xs+1][ysm1][zs ]; Potentialtype p221 = potentials[xs+1][ysp1][zs ]; Potentialtype p210 = potentials[xs+1][ys ][zsm1]; Potentialtype p212 = potentials[xs+1][ys ][zsp1]; double lirpfactor = ((double)threshold-p111)/(p211-p111); xeverts[xs][ys][zs][0] = (lirpfactor + xs)*cubiewidth+origin[0]; xeverts[xs][ys][zs][1] = ( ys)*cubiewidth+origin[1]; xeverts[xs][ys][zs][2] = ( zs)*cubiewidth+origin[2]; Normcoordtype nn[3]; nn[0] = (1-lirpfactor)*(p211-p011)+lirpfactor*(p311-p111); nn[1] = (1-lirpfactor)*(p121-p101)+lirpfactor*(p221-p201); nn[2] = (1-lirpfactor)*(p112-p110)+lirpfactor*(p212-p210); Normcoordtype len = sqrt(nn[0]*nn[0]+nn[1]*nn[1]+nn[2]*nn[2]); if (len > 0) { xenorms[xs][ys][zs][0] = -nn[0]/len; xenorms[xs][ys][zs][1] = -nn[1]/len; xenorms[xs][ys][zs][2] = -nn[2]/len; } else { xenorms[xs][ys][zs][0] = 1; xenorms[xs][ys][zs][1] = 0; xenorms[xs][ys][zs][2] = 0; } } // calcYintersection // See calcXintersection, above template inline void Cube::calcYintersection(int xs, int ys, int zs) { int ysm1 = (ys==0) ? ys : ys-1; int ysp2 = (ys==POTSIDE-2) ? ys+1 : ys+2; int xsm1 = (xs==0) ? xs : xs-1; int xsp1 = (xs==POTSIDE-1) ? xs : xs+1; int zsm1 = (zs==0) ? zs : zs-1; int zsp1 = (zs==POTSIDE-1) ? zs : zs+1; Potentialtype p011 = potentials[xs ][ysm1][zs ]; Potentialtype p111 = potentials[xs ][ys ][zs ]; Potentialtype p211 = potentials[xs ][ys+1][zs ]; Potentialtype p311 = potentials[xs ][ysp2][zs ]; Potentialtype p101 = potentials[xsm1][ys ][zs ]; Potentialtype p121 = potentials[xsp1][ys ][zs ]; Potentialtype p110 = potentials[xs ][ys ][zsm1]; Potentialtype p112 = potentials[xs ][ys ][zsp1]; Potentialtype p201 = potentials[xsm1][ys+1][zs ]; Potentialtype p221 = potentials[xsp1][ys+1][zs ]; Potentialtype p210 = potentials[xs ][ys+1][zsm1]; Potentialtype p212 = potentials[xs ][ys+1][zsp1]; double lirpfactor = ((double)threshold-p111)/(p211-p111); yeverts[xs][ys][zs][0] = ( xs)*cubiewidth+origin[0]; yeverts[xs][ys][zs][1] = (lirpfactor + ys)*cubiewidth+origin[1]; yeverts[xs][ys][zs][2] = ( zs)*cubiewidth+origin[2]; Normcoordtype nn[3]; nn[1] = (1-lirpfactor)*(p211-p011)+lirpfactor*(p311-p111); nn[0] = (1-lirpfactor)*(p121-p101)+lirpfactor*(p221-p201); nn[2] = (1-lirpfactor)*(p112-p110)+lirpfactor*(p212-p210); Normcoordtype len = sqrt(nn[0]*nn[0]+nn[1]*nn[1]+nn[2]*nn[2]); if (len > 0) { yenorms[xs][ys][zs][0] = -nn[0]/len; yenorms[xs][ys][zs][1] = -nn[1]/len; yenorms[xs][ys][zs][2] = -nn[2]/len; } else { yenorms[xs][ys][zs][0] = 1; yenorms[xs][ys][zs][1] = 0; yenorms[xs][ys][zs][2] = 0; } } // calcZintersection // See calcXintersection, above template inline void Cube::calcZintersection(int xs, int ys, int zs) { int zsm1 = (zs==0) ? zs : zs-1; int zsp2 = (zs==POTSIDE-2) ? zs+1 : zs+2; int xsm1 = (xs==0) ? xs : xs-1; int xsp1 = (xs==POTSIDE-1) ? xs : xs+1; int ysm1 = (ys==0) ? ys : ys-1; int ysp1 = (ys==POTSIDE-1) ? ys : ys+1; Potentialtype p011 = potentials[xs ][ys ][zsm1]; Potentialtype p111 = potentials[xs ][ys ][zs ]; Potentialtype p211 = potentials[xs ][ys ][zs+1]; Potentialtype p311 = potentials[xs ][ys ][zsp2]; Potentialtype p101 = potentials[xsm1][ys ][zs ]; Potentialtype p121 = potentials[xsp1][ys ][zs ]; Potentialtype p110 = potentials[xs ][ysm1][zs ]; Potentialtype p112 = potentials[xs ][ysp1][zs ]; Potentialtype p201 = potentials[xsm1][ys ][zs+1]; Potentialtype p221 = potentials[xsp1][ys ][zs+1]; Potentialtype p210 = potentials[xs ][ysm1][zs+1]; Potentialtype p212 = potentials[xs ][ysp1][zs+1]; double lirpfactor = ((double)threshold-p111)/(p211-p111); zeverts[xs][ys][zs][0] = ( xs)*cubiewidth+origin[0]; zeverts[xs][ys][zs][1] = ( ys)*cubiewidth+origin[1]; zeverts[xs][ys][zs][2] = (lirpfactor + zs)*cubiewidth+origin[2]; Normcoordtype nn[3]; nn[2] = (1-lirpfactor)*(p211-p011)+lirpfactor*(p311-p111); nn[0] = (1-lirpfactor)*(p121-p101)+lirpfactor*(p221-p201); nn[1] = (1-lirpfactor)*(p112-p110)+lirpfactor*(p212-p210); Normcoordtype len = sqrt(nn[0]*nn[0]+nn[1]*nn[1]+nn[2]*nn[2]); if (len > 0) { zenorms[xs][ys][zs][0] = -nn[0]/len; zenorms[xs][ys][zs][1] = -nn[1]/len; zenorms[xs][ys][zs][2] = -nn[2]/len; } else { zenorms[xs][ys][zs][0] = 1; zenorms[xs][ys][zs][1] = 0; zenorms[xs][ys][zs][2] = 0; } } template inline void Cube::getcubieinfo(const Potentialtype potvals[8], int & edgebitlist, const int * & trilist, int & trilistmaxsize) { int potbits = 0; if (potvals[0] < threshold) potbits |= 1; if (potvals[1] < threshold) potbits |= 2; if (potvals[2] < threshold) potbits |= 4; if (potvals[3] < threshold) potbits |= 8; if (potvals[4] < threshold) potbits |= 16; if (potvals[5] < threshold) potbits |= 32; if (potvals[6] < threshold) potbits |= 64; if (potvals[7] < threshold) potbits |= 128; edgebitlist = edgetable[potbits]; trilist = tritable[potbits]; trilistmaxsize = 15; } template void Cube::recalccubie(int n) { int ii, jj; Potentialtype mypots[8]; Vertcoordtype * everts[12]; Normcoordtype * enorms[12]; int xsub = vertsubstable[n][0]; int ysub = vertsubstable[n][1]; int zsub = vertsubstable[n][2]; mypots[0] = potentials[xsub ][ysub ][zsub ]; mypots[1] = potentials[xsub ][ysub+1][zsub ]; mypots[2] = potentials[xsub+1][ysub+1][zsub ]; mypots[3] = potentials[xsub+1][ysub ][zsub ]; mypots[4] = potentials[xsub ][ysub ][zsub+1]; mypots[5] = potentials[xsub ][ysub+1][zsub+1]; mypots[6] = potentials[xsub+1][ysub+1][zsub+1]; mypots[7] = potentials[xsub+1][ysub ][zsub+1]; int edgebitlist; const int * trilist; int trilistmaxsize; getcubieinfo(mypots, edgebitlist, trilist, trilistmaxsize); // Below, we assume that cubies are re-calc'd in lo-to-hi order. // Thus, when re-calc'ing a cube, all but 3 of its edges have // already been handled; we can assume that the correct intersection // location has been stored in the [xyz]everts arrays. // recalccubie() is called only by update() and stdowndate(), so // these two need to be (and, in fact, are) written accordingly. if (edgebitlist != 0) { // For efficiency: below only needed for small Y & Z if (edgebitlist & 8) // edge 3: xyz(0)-Xyz(3) { everts[ 3] = xeverts[xsub ][ysub ][zsub ]; enorms[ 3] = xenorms[xsub ][ysub ][zsub ]; if (ysub == 0 && zsub == 0) calcXintersection(xsub ,ysub ,zsub ); } // For efficiency: below only needed for small X & Z if (edgebitlist & 1) // edge 0: xyz(0)-xYz(1) { everts[ 0] = yeverts[xsub ][ysub ][zsub ]; enorms[ 0] = yenorms[xsub ][ysub ][zsub ]; if (xsub == 0 && zsub == 0) calcYintersection(xsub ,ysub ,zsub ); } // For efficiency: below only needed for small X & Y if (edgebitlist & 256) // edge 8: xyz(0)-xyZ(4) { everts[ 8] = zeverts[xsub ][ysub ][zsub ]; enorms[ 8] = zenorms[xsub ][ysub ][zsub ]; if (xsub == 0 && ysub == 0) calcZintersection(xsub ,ysub ,zsub ); } // For efficiency: below only needed for small X if (edgebitlist & 512) // edge 9: xYz(1)-xYZ(5) { everts[ 9] = zeverts[xsub ][ysub+1][zsub ]; enorms[ 9] = zenorms[xsub ][ysub+1][zsub ]; if (xsub == 0) calcZintersection(xsub ,ysub+1,zsub ); } if (edgebitlist & 16) // edge 4: xyZ(4)-xYZ(5) { everts[ 4] = yeverts[xsub ][ysub ][zsub+1]; enorms[ 4] = yenorms[xsub ][ysub ][zsub+1]; if (xsub == 0) calcYintersection(xsub ,ysub ,zsub+1); } // For efficiency: below only needed for small Y if (edgebitlist & 2048) // edge 11: Xyz(3)-XyZ(7) { everts[11] = zeverts[xsub+1][ysub ][zsub ]; enorms[11] = zenorms[xsub+1][ysub ][zsub ]; if (ysub == 0) calcZintersection(xsub+1,ysub ,zsub ); } if (edgebitlist & 128) // edge 7: xyZ(4)-XyZ(7) { everts[ 7] = xeverts[xsub ][ysub ][zsub+1]; enorms[ 7] = xenorms[xsub ][ysub ][zsub+1]; if (ysub == 0) calcXintersection(xsub ,ysub ,zsub+1); } // For efficiency: below only needed for small Z if (edgebitlist & 4) // edge 2: Xyz(3)-XYz(2) { everts[ 2] = yeverts[xsub+1][ysub ][zsub ]; enorms[ 2] = yenorms[xsub+1][ysub ][zsub ]; if (zsub == 0) calcYintersection(xsub+1,ysub ,zsub ); } if (edgebitlist & 2) // edge 1: xYz(1)-XYz(2) { everts[ 1] = xeverts[xsub ][ysub+1][zsub ]; enorms[ 1] = xenorms[xsub ][ysub+1][zsub ]; if (zsub == 0) calcXintersection(xsub ,ysub+1,zsub ); } // Always need to calc edges below if (edgebitlist & 1024) // edge 10: XYz(2)-XYZ(6) { everts[10] = zeverts[xsub+1][ysub+1][zsub ]; enorms[10] = zenorms[xsub+1][ysub+1][zsub ]; calcZintersection(xsub+1,ysub+1,zsub ); } if (edgebitlist & 64) // edge 6: XyZ(7)-XYZ(6) { everts[ 6] = yeverts[xsub+1][ysub ][zsub+1]; enorms[ 6] = yenorms[xsub+1][ysub ][zsub+1]; calcYintersection(xsub+1,ysub ,zsub+1); } if (edgebitlist & 32) // edge 5: xYZ(5)-XYZ(6) { everts[ 5] = xeverts[xsub ][ysub+1][zsub+1]; enorms[ 5] = xenorms[xsub ][ysub+1][zsub+1]; calcXintersection(xsub ,ysub+1,zsub+1); } vector_Triangle & mytris = data[n].ld.tris; mytris.erase(mytris.begin(), mytris.end()); Triangle curtri; for (ii=0; ii!=trilistmaxsize && trilist[ii]!=-1; ii+=3) { for (jj=0; jj<3; ++jj) { // We reverse vertex order below; normal & front faces toward lo pot's curtri.verts[jj] = everts[trilist[ii+2-jj]]; curtri.norms[jj] = enorms[trilist[ii+2-jj]]; } Vertcoordtype v1[3], v2[3]; Normcoordtype nn[3], len; v1[0] = curtri.verts[1][0]-curtri.verts[0][0]; v1[1] = curtri.verts[1][1]-curtri.verts[0][1]; v1[2] = curtri.verts[1][2]-curtri.verts[0][2]; v2[0] = curtri.verts[2][0]-curtri.verts[0][0]; v2[1] = curtri.verts[2][1]-curtri.verts[0][1]; v2[2] = curtri.verts[2][2]-curtri.verts[0][2]; nn[0] = v1[1]*v2[2]-v1[2]*v2[1]; nn[1] = v1[2]*v2[0]-v1[0]*v2[2]; nn[2] = v1[0]*v2[1]-v1[1]*v2[0]; len = sqrt(nn[0]*nn[0] + nn[1]*nn[1] + nn[2]*nn[2]); if (len > 0) { curtri.facenorm[0] = nn[0]/len; curtri.facenorm[1] = nn[1]/len; curtri.facenorm[2] = nn[2]/len; } else { curtri.facenorm[0] = 1.; curtri.facenorm[1] = 0.; curtri.facenorm[2] = 0.; } mytris.push_back(curtri); } } Potentialtype maxval = mypots[0]; Potentialtype minval = mypots[0]; for (ii=1; ii<8; ++ii) { if (mypots[ii] > maxval) maxval = mypots[ii]; if (mypots[ii] < minval) minval = mypots[ii]; } data[n].maxv = maxval; data[n].minv = minval; } template int Cube::nodenumtable[Cube::SIDE][Cube::SIDE][Cube::SIDE]; template int Cube::vertsubstable[Cube::NODES][3]; // Two tables below taken from following: // File Name: CIsoSurface.cpp // Last Modified: 5/8/2000 // Author: Raghavendra Chandrashekara (based on source code provided // by Paul Bourke and Cory Gene Bloyd) // Email: rc99@doc.ic.ac.uk, rchandrashekara@hotmail.com // Original code by Cory Gene Bloyd marked as public domain. // File found at http://astronomy.swin.edu.au/pbourke/modelling/polygonise template const int Cube::edgetable[256] = { 0x0 , 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00, 0x190, 0x99 , 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90, 0x230, 0x339, 0x33 , 0x13a, 0x636, 0x73f, 0x435, 0x53c, 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30, 0x3a0, 0x2a9, 0x1a3, 0xaa , 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0, 0x460, 0x569, 0x663, 0x76a, 0x66 , 0x16f, 0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60, 0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0xff , 0x3f5, 0x2fc, 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0, 0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x55 , 0x15c, 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950, 0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0xcc , 0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0, 0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc, 0xcc , 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0, 0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c, 0x15c, 0x55 , 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650, 0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5, 0xff , 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0, 0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x66 , 0x76a, 0x663, 0x569, 0x460, 0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac, 0x4ac, 0x5a5, 0x6af, 0x7a6, 0xaa , 0x1a3, 0x2a9, 0x3a0, 0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x33 , 0x339, 0x230, 0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c, 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x99 , 0x190, 0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c, 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x0 }; template const int Cube::tritable[256][16] = { {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 8, 3, 9, 8, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 2, 10, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 8, 3, 2, 10, 8, 10, 9, 8, -1, -1, -1, -1, -1, -1, -1}, {3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 11, 2, 8, 11, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 11, 2, 1, 9, 11, 9, 8, 11, -1, -1, -1, -1, -1, -1, -1}, {3, 10, 1, 11, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 10, 1, 0, 8, 10, 8, 11, 10, -1, -1, -1, -1, -1, -1, -1}, {3, 9, 0, 3, 11, 9, 11, 10, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 3, 0, 7, 3, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 1, 9, 4, 7, 1, 7, 3, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 4, 7, 3, 0, 4, 1, 2, 10, -1, -1, -1, -1, -1, -1, -1}, {9, 2, 10, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1}, {2, 10, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, -1}, {8, 4, 7, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 4, 7, 11, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 1, 8, 4, 7, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1}, {4, 7, 11, 9, 4, 11, 9, 11, 2, 9, 2, 1, -1, -1, -1, -1}, {3, 10, 1, 3, 11, 10, 7, 8, 4, -1, -1, -1, -1, -1, -1, -1}, {1, 11, 10, 1, 4, 11, 1, 0, 4, 7, 11, 4, -1, -1, -1, -1}, {4, 7, 8, 9, 0, 11, 9, 11, 10, 11, 0, 3, -1, -1, -1, -1}, {4, 7, 11, 4, 11, 9, 9, 11, 10, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 5, 4, 1, 5, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 5, 4, 8, 3, 5, 3, 1, 5, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 1, 2, 10, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1}, {5, 2, 10, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, -1}, {2, 10, 5, 3, 2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, -1}, {9, 5, 4, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 11, 2, 0, 8, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, -1}, {0, 5, 4, 0, 1, 5, 2, 3, 11, -1, -1, -1, -1, -1, -1, -1}, {2, 1, 5, 2, 5, 8, 2, 8, 11, 4, 8, 5, -1, -1, -1, -1}, {10, 3, 11, 10, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 5, 0, 8, 1, 8, 10, 1, 8, 11, 10, -1, -1, -1, -1}, {5, 4, 0, 5, 0, 11, 5, 11, 10, 11, 0, 3, -1, -1, -1, -1}, {5, 4, 8, 5, 8, 10, 10, 8, 11, -1, -1, -1, -1, -1, -1, -1}, {9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 3, 0, 9, 5, 3, 5, 7, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, -1}, {1, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 7, 8, 9, 5, 7, 10, 1, 2, -1, -1, -1, -1, -1, -1, -1}, {10, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3, -1, -1, -1, -1}, {8, 0, 2, 8, 2, 5, 8, 5, 7, 10, 5, 2, -1, -1, -1, -1}, {2, 10, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1, -1, -1}, {7, 9, 5, 7, 8, 9, 3, 11, 2, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 11, -1, -1, -1, -1}, {2, 3, 11, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, -1}, {11, 2, 1, 11, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 8, 8, 5, 7, 10, 1, 3, 10, 3, 11, -1, -1, -1, -1}, {5, 7, 0, 5, 0, 9, 7, 11, 0, 1, 0, 10, 11, 10, 0, -1}, {11, 10, 0, 11, 0, 3, 10, 5, 0, 8, 0, 7, 5, 7, 0, -1}, {11, 10, 5, 7, 11, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 1, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 8, 3, 1, 9, 8, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 5, 2, 6, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 5, 1, 2, 6, 3, 0, 8, -1, -1, -1, -1, -1, -1, -1}, {9, 6, 5, 9, 0, 6, 0, 2, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, -1}, {2, 3, 11, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 0, 8, 11, 2, 0, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 1, 9, 2, 9, 11, 2, 9, 8, 11, -1, -1, -1, -1}, {6, 3, 11, 6, 5, 3, 5, 1, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 11, 0, 11, 5, 0, 5, 1, 5, 11, 6, -1, -1, -1, -1}, {3, 11, 6, 0, 3, 6, 0, 6, 5, 0, 5, 9, -1, -1, -1, -1}, {6, 5, 9, 6, 9, 11, 11, 9, 8, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 3, 0, 4, 7, 3, 6, 5, 10, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 5, 10, 6, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1}, {10, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, -1}, {6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, -1}, {8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, -1}, {7, 3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, -1}, {3, 11, 2, 7, 8, 4, 10, 6, 5, -1, -1, -1, -1, -1, -1, -1}, {5, 10, 6, 4, 7, 2, 4, 2, 0, 2, 7, 11, -1, -1, -1, -1}, {0, 1, 9, 4, 7, 8, 2, 3, 11, 5, 10, 6, -1, -1, -1, -1}, {9, 2, 1, 9, 11, 2, 9, 4, 11, 7, 11, 4, 5, 10, 6, -1}, {8, 4, 7, 3, 11, 5, 3, 5, 1, 5, 11, 6, -1, -1, -1, -1}, {5, 1, 11, 5, 11, 6, 1, 0, 11, 7, 11, 4, 0, 4, 11, -1}, {0, 5, 9, 0, 6, 5, 0, 3, 6, 11, 6, 3, 8, 4, 7, -1}, {6, 5, 9, 6, 9, 11, 4, 7, 9, 7, 11, 9, -1, -1, -1, -1}, {10, 4, 9, 6, 4, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 10, 6, 4, 9, 10, 0, 8, 3, -1, -1, -1, -1, -1, -1, -1}, {10, 0, 1, 10, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, -1}, {8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 10, -1, -1, -1, -1}, {1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, -1}, {0, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1}, {10, 4, 9, 10, 6, 4, 11, 2, 3, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 2, 2, 8, 11, 4, 9, 10, 4, 10, 6, -1, -1, -1, -1}, {3, 11, 2, 0, 1, 6, 0, 6, 4, 6, 1, 10, -1, -1, -1, -1}, {6, 4, 1, 6, 1, 10, 4, 8, 1, 2, 1, 11, 8, 11, 1, -1}, {9, 6, 4, 9, 3, 6, 9, 1, 3, 11, 6, 3, -1, -1, -1, -1}, {8, 11, 1, 8, 1, 0, 11, 6, 1, 9, 1, 4, 6, 4, 1, -1}, {3, 11, 6, 3, 6, 0, 0, 6, 4, -1, -1, -1, -1, -1, -1, -1}, {6, 4, 8, 11, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 10, 6, 7, 8, 10, 8, 9, 10, -1, -1, -1, -1, -1, -1, -1}, {0, 7, 3, 0, 10, 7, 0, 9, 10, 6, 7, 10, -1, -1, -1, -1}, {10, 6, 7, 1, 10, 7, 1, 7, 8, 1, 8, 0, -1, -1, -1, -1}, {10, 6, 7, 10, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1, -1}, {2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, -1}, {7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, -1}, {7, 3, 2, 6, 7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 11, 10, 6, 8, 10, 8, 9, 8, 6, 7, -1, -1, -1, -1}, {2, 0, 7, 2, 7, 11, 0, 9, 7, 6, 7, 10, 9, 10, 7, -1}, {1, 8, 0, 1, 7, 8, 1, 10, 7, 6, 7, 10, 2, 3, 11, -1}, {11, 2, 1, 11, 1, 7, 10, 6, 1, 6, 7, 1, -1, -1, -1, -1}, {8, 9, 6, 8, 6, 7, 9, 1, 6, 11, 6, 3, 1, 3, 6, -1}, {0, 9, 1, 11, 6, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 8, 0, 7, 0, 6, 3, 11, 0, 11, 6, 0, -1, -1, -1, -1}, {7, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 8, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 9, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 1, 9, 8, 3, 1, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1}, {10, 1, 2, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 3, 0, 8, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1}, {2, 9, 0, 2, 10, 9, 6, 11, 7, -1, -1, -1, -1, -1, -1, -1}, {6, 11, 7, 2, 10, 3, 10, 8, 3, 10, 9, 8, -1, -1, -1, -1}, {7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1, -1, -1, -1, -1, -1}, {2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, -1}, {1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1, -1, -1, -1}, {10, 7, 6, 10, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, -1}, {10, 7, 6, 1, 7, 10, 1, 8, 7, 1, 0, 8, -1, -1, -1, -1}, {0, 3, 7, 0, 7, 10, 0, 10, 9, 6, 10, 7, -1, -1, -1, -1}, {7, 6, 10, 7, 10, 8, 8, 10, 9, -1, -1, -1, -1, -1, -1, -1}, {6, 8, 4, 11, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 6, 11, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1, -1}, {8, 6, 11, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, -1}, {9, 4, 6, 9, 6, 3, 9, 3, 1, 11, 3, 6, -1, -1, -1, -1}, {6, 8, 4, 6, 11, 8, 2, 10, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 3, 0, 11, 0, 6, 11, 0, 4, 6, -1, -1, -1, -1}, {4, 11, 8, 4, 6, 11, 0, 2, 9, 2, 10, 9, -1, -1, -1, -1}, {10, 9, 3, 10, 3, 2, 9, 4, 3, 11, 3, 6, 4, 6, 3, -1}, {8, 2, 3, 8, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1}, {0, 4, 2, 4, 6, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 9, 0, 2, 3, 4, 2, 4, 6, 4, 3, 8, -1, -1, -1, -1}, {1, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, -1}, {8, 1, 3, 8, 6, 1, 8, 4, 6, 6, 10, 1, -1, -1, -1, -1}, {10, 1, 0, 10, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, -1}, {4, 6, 3, 4, 3, 8, 6, 10, 3, 0, 3, 9, 10, 9, 3, -1}, {10, 9, 4, 6, 10, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 5, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 4, 9, 5, 11, 7, 6, -1, -1, -1, -1, -1, -1, -1}, {5, 0, 1, 5, 4, 0, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1}, {11, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, -1}, {9, 5, 4, 10, 1, 2, 7, 6, 11, -1, -1, -1, -1, -1, -1, -1}, {6, 11, 7, 1, 2, 10, 0, 8, 3, 4, 9, 5, -1, -1, -1, -1}, {7, 6, 11, 5, 4, 10, 4, 2, 10, 4, 0, 2, -1, -1, -1, -1}, {3, 4, 8, 3, 5, 4, 3, 2, 5, 10, 5, 2, 11, 7, 6, -1}, {7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 5, 4, 0, 8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, -1}, {3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, -1}, {6, 2, 8, 6, 8, 7, 2, 1, 8, 4, 8, 5, 1, 5, 8, -1}, {9, 5, 4, 10, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, -1}, {1, 6, 10, 1, 7, 6, 1, 0, 7, 8, 7, 0, 9, 5, 4, -1}, {4, 0, 10, 4, 10, 5, 0, 3, 10, 6, 10, 7, 3, 7, 10, -1}, {7, 6, 10, 7, 10, 8, 5, 4, 10, 4, 8, 10, -1, -1, -1, -1}, {6, 9, 5, 6, 11, 9, 11, 8, 9, -1, -1, -1, -1, -1, -1, -1}, {3, 6, 11, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, -1}, {0, 11, 8, 0, 5, 11, 0, 1, 5, 5, 6, 11, -1, -1, -1, -1}, {6, 11, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 10, 9, 5, 11, 9, 11, 8, 11, 5, 6, -1, -1, -1, -1}, {0, 11, 3, 0, 6, 11, 0, 9, 6, 5, 6, 9, 1, 2, 10, -1}, {11, 8, 5, 11, 5, 6, 8, 0, 5, 10, 5, 2, 0, 2, 5, -1}, {6, 11, 3, 6, 3, 5, 2, 10, 3, 10, 5, 3, -1, -1, -1, -1}, {5, 8, 9, 5, 2, 8, 5, 6, 2, 3, 8, 2, -1, -1, -1, -1}, {9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, -1}, {1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8, 2, 6, 2, 8, -1}, {1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 3, 6, 1, 6, 10, 3, 8, 6, 5, 6, 9, 8, 9, 6, -1}, {10, 1, 0, 10, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, -1}, {0, 3, 8, 5, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {10, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 5, 10, 7, 5, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {11, 5, 10, 11, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, -1}, {5, 11, 7, 5, 10, 11, 1, 9, 0, -1, -1, -1, -1, -1, -1, -1}, {10, 7, 5, 10, 11, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, -1}, {11, 1, 2, 11, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 11, -1, -1, -1, -1}, {9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 11, 7, -1, -1, -1, -1}, {7, 5, 2, 7, 2, 11, 5, 9, 2, 3, 2, 8, 9, 8, 2, -1}, {2, 5, 10, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1}, {8, 2, 0, 8, 5, 2, 8, 7, 5, 10, 2, 5, -1, -1, -1, -1}, {9, 0, 1, 5, 10, 3, 5, 3, 7, 3, 10, 2, -1, -1, -1, -1}, {9, 8, 2, 9, 2, 1, 8, 7, 2, 10, 2, 5, 7, 5, 2, -1}, {1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 7, 0, 7, 1, 1, 7, 5, -1, -1, -1, -1, -1, -1, -1}, {9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, -1}, {9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {5, 8, 4, 5, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1}, {5, 0, 4, 5, 11, 0, 5, 10, 11, 11, 3, 0, -1, -1, -1, -1}, {0, 1, 9, 8, 4, 10, 8, 10, 11, 10, 4, 5, -1, -1, -1, -1}, {10, 11, 4, 10, 4, 5, 11, 3, 4, 9, 4, 1, 3, 1, 4, -1}, {2, 5, 1, 2, 8, 5, 2, 11, 8, 4, 5, 8, -1, -1, -1, -1}, {0, 4, 11, 0, 11, 3, 4, 5, 11, 2, 11, 1, 5, 1, 11, -1}, {0, 2, 5, 0, 5, 9, 2, 11, 5, 4, 5, 8, 11, 8, 5, -1}, {9, 4, 5, 2, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 5, 10, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, -1}, {5, 10, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, -1}, {3, 10, 2, 3, 5, 10, 3, 8, 5, 4, 5, 8, 0, 1, 9, -1}, {5, 10, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, -1}, {8, 4, 5, 8, 5, 3, 3, 5, 1, -1, -1, -1, -1, -1, -1, -1}, {0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {8, 4, 5, 8, 5, 3, 9, 0, 5, 0, 3, 5, -1, -1, -1, -1}, {9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 11, 7, 4, 9, 11, 9, 10, 11, -1, -1, -1, -1, -1, -1, -1}, {0, 8, 3, 4, 9, 7, 9, 11, 7, 9, 10, 11, -1, -1, -1, -1}, {1, 10, 11, 1, 11, 4, 1, 4, 0, 7, 4, 11, -1, -1, -1, -1}, {3, 1, 4, 3, 4, 8, 1, 10, 4, 7, 4, 11, 10, 11, 4, -1}, {4, 11, 7, 9, 11, 4, 9, 2, 11, 9, 1, 2, -1, -1, -1, -1}, {9, 7, 4, 9, 11, 7, 9, 1, 11, 2, 11, 1, 0, 8, 3, -1}, {11, 7, 4, 11, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1, -1, -1}, {11, 7, 4, 11, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, -1}, {2, 9, 10, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, -1}, {9, 10, 7, 9, 7, 4, 10, 2, 7, 8, 7, 0, 2, 0, 7, -1}, {3, 7, 10, 3, 10, 2, 7, 4, 10, 1, 10, 0, 4, 0, 10, -1}, {1, 10, 2, 8, 7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, -1}, {4, 9, 1, 4, 1, 7, 0, 8, 1, 8, 7, 1, -1, -1, -1, -1}, {4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {4, 8, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {9, 10, 8, 10, 11, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 9, 3, 9, 11, 11, 9, 10, -1, -1, -1, -1, -1, -1, -1}, {0, 1, 10, 0, 10, 8, 8, 10, 11, -1, -1, -1, -1, -1, -1, -1}, {3, 1, 10, 11, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 2, 11, 1, 11, 9, 9, 11, 8, -1, -1, -1, -1, -1, -1, -1}, {3, 0, 9, 3, 9, 11, 1, 2, 9, 2, 11, 9, -1, -1, -1, -1}, {0, 2, 11, 8, 0, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {3, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 8, 2, 8, 10, 10, 8, 9, -1, -1, -1, -1, -1, -1, -1}, {9, 10, 2, 0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {2, 3, 8, 2, 8, 10, 0, 1, 8, 1, 10, 8, -1, -1, -1, -1}, {1, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {1, 3, 8, 9, 1, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 9, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {0, 3, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1}, {-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1} };