VarDataMarchCubes.cpp

#include "VarData.h"

//
// Marching Cubes Example Program 
// by Cory Bloyd (corysama@yahoo.com)
//
// A simple, portable and complete implementation of the Marching Cubes
// and Marching Tetrahedrons algorithms in a single source file.
// There are many ways that this code could be made faster, but the 
// intent is for the code to be easy to understand.
//
// For a description of the algorithm go to
// http://astronomy.swin.edu.au/pbourke/modelling/polygonise/
//
// This code is public domain.
//
XYZ VertexInterp(double isolevel,XYZ p1,XYZ p2,double valp1,double valp2);
int PolygoniseCube(GRIDCELL g,double iso,VAR_TRIANGLE *tri);
int PolygoniseSquare(GRIDCELL g,double iso,VAR_LINE *tri);
XYZ TriangNorm(XYZ p1,XYZ p2,XYZ p3);
VAR_TRIANGLE *VarData::MarchingCubes(double *Plot,int NSample,double IsoLevel,int *NTriang){
  int NTri = 0;
  double InvNSample = 1./(double)NSample;
  int NVertex = 2*NSample-1;
  GRIDCELL Grid;
  VAR_TRIANGLE triangles[10];
  VAR_TRIANGLE *Triang = NULL;
  for(int sx = 0;sx<NSample-1;sx++){
    for(int sy = 0;sy<NSample-1;sy++){
      for(int sz = 0;sz<NSample-1;sz++){
   Grid.p[0].x[0] = (sx)*InvNSample*pEdge(0);
   Grid.p[0].x[1] = (sy)*InvNSample*pEdge(1);
   Grid.p[0].x[2] = (sz)*InvNSample*pEdge(2);
   Grid.val[0] = Plot[((sx)*NSample+(sy))*NSample+sz];
   Grid.p[1].x[0] = (sx+1)*InvNSample*pEdge(0);
   Grid.p[1].x[1] = (sy)*InvNSample*pEdge(1);
   Grid.p[1].x[2] = (sz)*InvNSample*pEdge(2);
   Grid.val[1] = Plot[((sx+1)*NSample+(sy))*NSample+sz];
   Grid.p[2].x[0] = (sx+1)*InvNSample*pEdge(0);
   Grid.p[2].x[1] = (sy+1)*InvNSample*pEdge(1);
   Grid.p[2].x[2] = (sz)*InvNSample*pEdge(2);
   Grid.val[2] = Plot[((sx+1)*NSample+(sy+1))*NSample+sz];
   Grid.p[3].x[0] = (sx)*InvNSample*pEdge(0);
   Grid.p[3].x[1] = (sy+1)*InvNSample*pEdge(1);
   Grid.p[3].x[2] = (sz)*InvNSample*pEdge(2);
   Grid.val[3] = Plot[((sx)*NSample+(sy+1))*NSample+sz];
   Grid.p[4].x[0] = (sx)*InvNSample*pEdge(0);
   Grid.p[4].x[1] = (sy)*InvNSample*pEdge(1);
   Grid.p[4].x[2] = (sz+1)*InvNSample*pEdge(2);
   Grid.val[4] = Plot[((sx)*NSample+(sy))*NSample+sz+1];
   Grid.p[5].x[0] = (sx+1)*InvNSample*pEdge(0);
   Grid.p[5].x[1] = (sy)*InvNSample*pEdge(1);
   Grid.p[5].x[2] = (sz+1)*InvNSample*pEdge(2);
   Grid.val[5] = Plot[((sx+1)*NSample+(sy))*NSample+sz+1];
   Grid.p[6].x[0] = (sx+1)*InvNSample*pEdge(0);
   Grid.p[6].x[1] = (sy+1)*InvNSample*pEdge(1);
   Grid.p[6].x[2] = (sz+1)*InvNSample*pEdge(2);
   Grid.val[6] = Plot[((sx+1)*NSample+(sy+1))*NSample+sz+1];
   Grid.p[7].x[0] = (sx)*InvNSample*pEdge(0);
   Grid.p[7].x[1] = (sy+1)*InvNSample*pEdge(1);
   Grid.p[7].x[2] = (sz+1)*InvNSample*pEdge(2);
   Grid.val[7] = Plot[((sx)*NSample+(sy+1))*NSample+sz+1];
   int n = PolygoniseCube(Grid,IsoLevel,triangles);
   Triang = (VAR_TRIANGLE *)realloc(Triang,(NTri+n)*sizeof(VAR_TRIANGLE));
   int s[3];
   for(int l=0;l<n;l++){
     for(int v=0;v<3;v++){
       for(int d=0;d<3;d++){
         s[d] = (int)(triangles[l].p[v].x[d]*pInvEdge(d)*NVertex);
         if(s[d] < 0 || s[d] >= NVertex){
      printf("Marching: 0 <= sx %d < NVertex %d  0. < %lf < %lf\n",sx,NVertex,triangles[l].p[v].x[d],pEdge(d));
      continue;
         }
       }
       triangles[l].v[v] = (s[0]*NVertex+s[1])*NVertex+s[2];
     }
     Triang[NTri+l] = triangles[l];
   }
   NTri += n;
      }
    }
  }
  *NTriang = NTri;
  return Triang;
}
int PolygoniseCube(GRIDCELL g,double iso,VAR_TRIANGLE *tri){
  extern int edgeTable[256];
  extern int triTable[256][16];
  int i,ntri = 0;
  int cubeindex;
  XYZ vertlist[12];
  double OneThird = 1./3.;
  /*
    Determine the index into the edge table which
    tells us which vertices are inside of the surface
  */
  cubeindex = 0;
  if (g.val[0] < iso) cubeindex |= 1;
  if (g.val[1] < iso) cubeindex |= 2;
  if (g.val[2] < iso) cubeindex |= 4;
  if (g.val[3] < iso) cubeindex |= 8;
  if (g.val[4] < iso) cubeindex |= 16;
  if (g.val[5] < iso) cubeindex |= 32;
  if (g.val[6] < iso) cubeindex |= 64;
  if (g.val[7] < iso) cubeindex |= 128;

  /* Cube is entirely in/out of the surface */
  if (edgeTable[cubeindex] == 0)
    return(0);

  /* Find the vertices where the surface intersects the cube */
  if (edgeTable[cubeindex] & 1) {
    vertlist[0] = VertexInterp(iso,g.p[0],g.p[1],g.val[0],g.val[1]);
  }
  if (edgeTable[cubeindex] & 2) {
    vertlist[1] = VertexInterp(iso,g.p[1],g.p[2],g.val[1],g.val[2]);
  }
  if (edgeTable[cubeindex] & 4) {
    vertlist[2] = VertexInterp(iso,g.p[2],g.p[3],g.val[2],g.val[3]);
  }
  if (edgeTable[cubeindex] & 8) {
    vertlist[3] = VertexInterp(iso,g.p[3],g.p[0],g.val[3],g.val[0]);
  }
  if (edgeTable[cubeindex] & 16) {
    vertlist[4] = VertexInterp(iso,g.p[4],g.p[5],g.val[4],g.val[5]);
  }
  if (edgeTable[cubeindex] & 32) {
    vertlist[5] = VertexInterp(iso,g.p[5],g.p[6],g.val[5],g.val[6]);
  }
  if (edgeTable[cubeindex] & 64) {
    vertlist[6] = VertexInterp(iso,g.p[6],g.p[7],g.val[6],g.val[7]);
  }
  if (edgeTable[cubeindex] & 128) {
    vertlist[7] = VertexInterp(iso,g.p[7],g.p[4],g.val[7],g.val[4]);
  }
  if (edgeTable[cubeindex] & 256) {
    vertlist[8] = VertexInterp(iso,g.p[0],g.p[4],g.val[0],g.val[4]);
  }
  if (edgeTable[cubeindex] & 512) {
    vertlist[9] = VertexInterp(iso,g.p[1],g.p[5],g.val[1],g.val[5]);
  }
  if (edgeTable[cubeindex] & 1024) {
    vertlist[10] = VertexInterp(iso,g.p[2],g.p[6],g.val[2],g.val[6]);
  }
  if (edgeTable[cubeindex] & 2048) {
    vertlist[11] = VertexInterp(iso,g.p[3],g.p[7],g.val[3],g.val[7]);
  }
  /* Create the triangles */
  for (i=0;triTable[cubeindex][i]!=-1;i+=3) {
    tri[ntri].p[0] = vertlist[triTable[cubeindex][i  ]];
    tri[ntri].p[1] = vertlist[triTable[cubeindex][i+1]];
    tri[ntri].p[2] = vertlist[triTable[cubeindex][i+2]];
    for(int d=0;d<3;d++){
      tri[ntri].c.x[d] = (tri[ntri].p[0].x[d]+tri[ntri].p[1].x[d]+tri[ntri].p[2].x[d])*OneThird;
    }
    //TODO: Find the normal to the vertices, 
    // i.e. how the triangles are connected
    tri[ntri].n[0] = TriangNorm(tri[ntri].p[0],tri[ntri].p[1],tri[ntri].p[2]);
    tri[ntri].n[1] = TriangNorm(tri[ntri].p[0],tri[ntri].p[1],tri[ntri].p[2]);
    tri[ntri].n[2] = TriangNorm(tri[ntri].p[0],tri[ntri].p[1],tri[ntri].p[2]);
    //if(fabs(tri[ntri].n[0].x+tri[ntri].n[0].y+tri[ntri].n[0].z) <= 0.) continue;
    ntri++;
  }
  return(ntri);
}
VAR_LINE *VarData::MarchingSquares(double *Plot,int NSample,double IsoLevel,int *NTriang){
  int NTri = 0;
  double InvNSample = 1./(double)NSample;
  int NVertex = 2*NSample-1;
  GRIDCELL Grid;
  VAR_LINE triangles[4];
  VAR_LINE *Triang = NULL;
  for(int sx = 0;sx<NSample-1;sx++){
    for(int sy = 0;sy<NSample-1;sy++){
      Grid.p[0].x[0] = (sx)*InvNSample*pEdge(0);
      Grid.p[0].x[1] = (sy)*InvNSample*pEdge(1);
      Grid.p[0].x[2] = IsoLevel;
      Grid.val[0] = Plot[(sx)*NSample+(sy)];
      Grid.p[1].x[0] = (sx+1)*InvNSample*pEdge(0);
      Grid.p[1].x[1] = (sy)*InvNSample*pEdge(1);
      Grid.p[1].x[2] = IsoLevel;
      Grid.val[1] = Plot[(sx+1)*NSample+(sy)];
      Grid.p[2].x[0] = (sx+1)*InvNSample*pEdge(0);
      Grid.p[2].x[1] = (sy+1)*InvNSample*pEdge(1);
      Grid.p[2].x[2] = IsoLevel;
      Grid.val[2] = Plot[(sx+1)*NSample+(sy+1)];
      Grid.p[3].x[0] = (sx)*InvNSample*pEdge(0);
      Grid.p[3].x[1] = (sy+1)*InvNSample*pEdge(1);
      Grid.p[3].x[2] = IsoLevel;
      Grid.val[3] = Plot[(sx)*NSample+(sy+1)];
      int n = PolygoniseSquare(Grid,IsoLevel,triangles);
      Triang = (VAR_LINE *)realloc(Triang,(NTri+n)*sizeof(VAR_LINE));
      int s[3];
      for(int l=0;l<n;l++){
   for(int v=0;v<2;v++){
     for(int d=0;d<2;d++){
       s[d] = (int)(triangles[l].p[v].x[d]*pInvEdge(d)*NVertex);
       if(s[d] < 0 || s[d] >= NVertex){
         printf("Marching squares: 0 <= sx %d < NVertex %d  0. < %lf < %lf\n",s[d],NVertex,triangles[l].p[v].x[d],pEdge(d));
         continue;
       }
     }
     triangles[l].v[v] = s[0]*NVertex+s[1];
   }
   Triang[NTri+l] = triangles[l];
      }
      NTri += n;
    }
  }
  *NTriang = NTri;
  return Triang;
}
int PolygoniseSquare(GRIDCELL g,double iso,VAR_LINE *tri){
  extern int edgeTable2d[16];
  extern int triTable2d[16][4];
  int i,ntri = 0;
  int cubeindex;
  XYZ vertlist[4];
  XYZ Normal;
  Normal.x[0] = 0.;
  Normal.x[1] = 0.;
  Normal.x[2] = 1.;
  /*
    Determine the index into the edge table which
    tells us which vertices are inside of the surface
  */
  cubeindex = 0;
  if (g.val[0] < iso) cubeindex |= 1;
  if (g.val[1] < iso) cubeindex |= 2;
  if (g.val[2] < iso) cubeindex |= 4;
  if (g.val[3] < iso) cubeindex |= 8;
  /* Square is entirely in/out of the surface */
  if (edgeTable2d[cubeindex] == 0)
    return(0);
  /* Find the vertices where the surface intersects the cube */
  if (edgeTable2d[cubeindex] & 1) {
    vertlist[0] = VertexInterp(iso,g.p[0],g.p[1],g.val[0],g.val[1]);
  }
  if (edgeTable2d[cubeindex] & 2) {
    vertlist[1] = VertexInterp(iso,g.p[1],g.p[2],g.val[1],g.val[2]);
  }
  if (edgeTable2d[cubeindex] & 4) {
    vertlist[2] = VertexInterp(iso,g.p[2],g.p[3],g.val[2],g.val[3]);
  }
  if (edgeTable2d[cubeindex] & 8) {
    vertlist[3] = VertexInterp(iso,g.p[3],g.p[0],g.val[3],g.val[0]);
  }
  /* Create the triangles */
  for(i=0;triTable2d[cubeindex][i]!=-1;i+=2){
    tri[ntri].p[0] = vertlist[triTable2d[cubeindex][i  ]];
    tri[ntri].p[1] = vertlist[triTable2d[cubeindex][i+1]];
    for(int d=0;d<2;d++){
      tri[ntri].c.x[d] = (tri[ntri].p[0].x[d]+tri[ntri].p[1].x[d])*.5;
    }
    //TODO: Find the normal to the vertices, 
    // i.e. how the triangles are connected
    tri[ntri].n[0] = Normal;
    tri[ntri].n[1] = Normal;
    //if(fabs(tri[ntri].n[0].x+tri[ntri].n[0].y+tri[ntri].n[0].z) <= 0.) continue;
    ntri++;
  }
  return(ntri);
}
XYZ TriangNorm(XYZ p1,XYZ p2,XYZ p3){
  XYZ n;
  double Norm = 0.;
  n.x[0] = (p2.x[1]-p1.x[1])*(p2.x[2]-p3.x[2]) 
    - (p2.x[1]-p3.x[1])*(p2.x[2]-p1.x[2]);
  n.x[1] = (p2.x[2]-p1.x[2])*(p2.x[0]-p3.x[0]) 
    - (p2.x[2]-p3.x[2])*(p2.x[0]-p1.x[0]);
  n.x[2] = (p2.x[0]-p1.x[0])*(p2.x[1]-p3.x[1]) 
    - (p2.x[0]-p3.x[0])*(p2.x[1]-p1.x[1]);
  Norm = sqrt(SQR(n.x[0])+SQR(n.x[1])+SQR(n.x[2]));
  if(Norm > 0.){
    Norm = 1./Norm;
    n.x[0] *= Norm;
    n.x[1] *= Norm;
    n.x[2] *= Norm;
  }
  return n;
}
XYZ VertexInterp(double isolevel,XYZ p1,XYZ p2,double valp1,double valp2){
  double mu;
  XYZ p;
  if (ABS(isolevel-valp1) < 0.00001)
    return(p1);
  if (ABS(isolevel-valp2) < 0.00001)
    return(p2);
  if (ABS(valp1-valp2) < 0.00001)
    return(p1);
  mu = (isolevel - valp1) / (valp2 - valp1);
  p.x[0] = p1.x[0] + mu * (p2.x[0] - p1.x[0]);
  p.x[1] = p1.x[1] + mu * (p2.x[1] - p1.x[1]);
  p.x[2] = p1.x[2] + mu * (p2.x[2] - p1.x[2]);
  return(p);
}
int 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   
};
int 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}
};
int edgeTable2d[16]={
  0x0 , 0x09, 0x03, 0x0a, 0x06, 0x0f, 0x05, 0x0c, 
  0x0c, 0x05, 0x0f, 0x06, 0x0a, 0x03, 0x09, 0x0
};
int triTable2d[16][4] = {
  {-1,-1,-1,-1},
  {0,3,-1,-1},
  {0,1,-1,-1},
  {3,1,-1,-1},
  {1,2,-1,-1},
  {0,1,2,3},
  {0,2,-1,-1},
  {2,3,-1,-1},
  {2,3,-1,-1},
  {2,0,-1,-1},
  {3,0,1,2},
  {1,2,-1,-1},
  {1,3,-1,-1},
  {0,1,-1,-1},
  {3,0,-1,-1},
  {-1,-1,-1,-1}
};