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MarchingCubes.cs
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MarchingCubes.cs
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using System.Collections.Generic;
using System;
namespace Mola
{
public class MarchingCube
{
public static float V(double v1, double v2, double iso)
{
if (Math.Abs(v2 - v1) < 0.0000001f)
return 0;
return (float)((iso - v1) / (v2 - v1));
}
private static int Offset(double[] n, double iso)
{
int caseNumber = 0;
for (int i = 7; i > -1; i--)
{
if (n[i] > iso)
{
caseNumber++;
}
if (i > 0)
{
caseNumber = caseNumber << 1;
}
}
// collecting the faces
return caseNumber * 15;
}
public static MolaMesh MarchingCubesMesh(int nX, int nY, int nZ, List<double> values, float iso, float x1, float y1, float z1, float x2, float y2, float z2)
{
MolaMesh mesh = new MolaMesh();
float dimX = (x2 - x1) / (nX - 1);
float dimY = (y2 - y1) / (nY - 1);
float dimZ = (z2 - z1) / (nZ - 1);
int nYZ = nY * nZ;
int index = 0;
double[] n = new double[8];
float pX = 0;
float pY = 0;
float pZ = 0;
for (int x = 0; x < nX - 1; x++)
{
int cX = x * nYZ;
for (int y = 0; y < nY - 1; y++)
{
int addZ = cX + y * nZ;
for (int z = 0; z < nZ - 1; z++)
{
index = z + addZ;// or just index++?
// collecting the values
n[0] = values[index + nZ]; // 0,1,0
n[1] = values[index + nYZ + nZ]; // 1,1,0
n[2] = values[index + nYZ]; // 1,0,0
n[3] = values[index]; // 0,0,0
n[4] = values[index + nZ + 1]; // 0,1,1
n[5] = values[index + nYZ + nZ + 1]; // 1,1,1
n[6] = values[index + nYZ + 1]; // 1,0,1
n[7] = values[index + 1]; // 0,0,1
// collecting the faces
int offset = Offset(n, iso);
for (int i = offset; i < offset + 15; i += 3)
{
if (faces[i] > -1)
{
// List<int> vs = new List<int>();
for (int j = i; j < i + 3; j++)
{
switch (faces[j])
{
// horizontal bottom
case 0:
pX = x + V(n[0], n[1], iso);
pY = y + 1;
pZ = z;
break;
case 1:
pX = x + 1;
pY = y + V(n[2], n[1], iso);
pZ = z;
break;
case 2:
pX = x + V(n[3], n[2], iso);
pY = y;
pZ = z;
break;
case 3:
pX = x;
pY = y + V(n[3], n[0], iso);
pZ = z;
break;
// horizontal top
case 4:
pX = x + V(n[4], n[5], iso);
pY = y + 1;
pZ = z + 1;
break;
case 5:
pX = x + 1;
pY = y + V(n[6], n[5], iso);
pZ = z + 1;
break;
case 6:
pX = x + V(n[7], n[6], iso);
pY = y;
pZ = z + 1;
break;
case 7:
pX = x;
pY = y + V(n[7], n[4], iso);
pZ = z + 1;
break;
// vertical
case 8:
pX = x;
pY = y + 1;
pZ = z + V(n[0], n[4], iso);
break;
case 9:
pX = x + 1;
pY = y + 1;
pZ = z + V(n[1], n[5], iso);
break;
case 10:
pX = x;
pY = y;
pZ = z + V(n[3], n[7], iso);
break;
case 11:
pX = x + 1;
pY = y;
pZ = z + V(n[2], n[6], iso);
break;
default:
break;
}
mesh.AddVertex(pX * dimX + x1, pY * dimY + y1, pZ * dimZ + z1);
}
}
}
}
}
}
for (int i = 0; i < mesh.VertexCount(); i += 3)
{
mesh.AddTriangle(i, i + 1, i + 2);
}
return mesh;
}
private static void CollectFaces(double[] n, int x, int y, int z, double iso, List<float[]> coordinates)
{
int offset = Offset(n, iso);
float pX = 0;
float pY = 0;
float pZ = 0;
for (int i = offset; i < offset + 15; i += 3)
{
if (faces[i] > -1)
{
// List<int> vs = new List<int>();
for (int j = i + 2; j >= i; j--)
{
switch (faces[j])
{
// horizontal bottom
case 0:
pX = x + V(n[0], n[1], iso);
pY = y + 1;
pZ = z;
break;
case 1:
pX = x + 1;
pY = y + V(n[2], n[1], iso);
pZ = z;
break;
case 2:
pX = x + V(n[3], n[2], iso);
pY = y;
pZ = z;
break;
case 3:
pX = x;
pY = y + V(n[3], n[0], iso);
pZ = z;
break;
// horizontal top
case 4:
pX = x + V(n[4], n[5], iso);
pY = y + 1;
pZ = z + 1;
break;
case 5:
pX = x + 1;
pY = y + V(n[6], n[5], iso);
pZ = z + 1;
break;
case 6:
pX = x + V(n[7], n[6], iso);
pY = y;
pZ = z + 1;
break;
case 7:
pX = x;
pY = y + V(n[7], n[4], iso);
pZ = z + 1;
break;
// vertical
case 8:
pX = x;
pY = y + 1;
pZ = z + V(n[0], n[4], iso);
break;
case 9:
pX = x + 1;
pY = y + 1;
pZ = z + V(n[1], n[5], iso);
break;
case 10:
pX = x;
pY = y;
pZ = z + V(n[3], n[7], iso);
break;
case 11:
pX = x + 1;
pY = y;
pZ = z + V(n[2], n[6], iso);
break;
default:
break;
}
coordinates.Add(new float[] { pX, pY, pZ });
}
}
}
}
public static List<float[]> MarchingCubes(float[,,] values, float iso)
{
double[] n = new double[8];
List<float[]> coordinates = new List<float[]>();
int nX = values.GetLength(0);
int nY = values.GetLength(1);
int nZ = values.GetLength(2);
for (int x = 0; x < nX - 1; x++)
{
for (int y = 0; y < nY - 1; y++)
{
for (int z = 0; z < nZ - 1; z++)
{
// collecting the values
n[0] = values[x, y + 1, z]; // 0,1,0
n[1] = values[x + 1, y + 1, z]; // 1,1,0
n[2] = values[x + 1, y, z]; // 1,0,0
n[3] = values[x, y, z]; // 0,0,0
n[4] = values[x, y + 1, z + 1]; // 0,1,1
n[5] = values[x + 1, y + 1, z + 1]; // 1,1,1
n[6] = values[x + 1, y, z + 1]; // 1,0,1
n[7] = values[x, y, z + 1]; // 0,0,1
CollectFaces(n, x, y, z, iso, coordinates);
}
}
}
return coordinates;
}
public static List<float[]> MarchingCubes(int nX, int nY, int nZ, List<float> values, float iso)
{
int nYZ = nY * nZ;
int index = 0;
double[] n = new double[8];
List<float[]> coordinates = new List<float[]>();
for (int x = 0; x < nX - 1; x++)
{
int cX = x * nYZ;
for (int y = 0; y < nY - 1; y++)
{
int addZ = cX + y * nZ;
for (int z = 0; z < nZ - 1; z++)
{
index = z + addZ;// or just index++?
// collecting the values
n[0] = values[index + nZ]; // 0,1,0
n[1] = values[index + nYZ + nZ]; // 1,1,0
n[2] = values[index + nYZ]; // 1,0,0
n[3] = values[index]; // 0,0,0
n[4] = values[index + nZ + 1]; // 0,1,1
n[5] = values[index + nYZ + nZ + 1]; // 1,1,1
n[6] = values[index + nYZ + 1]; // 1,0,1
n[7] = values[index + 1]; // 0,0,1
CollectFaces(n, x, y, z, iso, coordinates);
}
}
}
return coordinates;
}
public static int[] faces = { -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, 0, 1, 9, -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, 2, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 3, 1, 2,
11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 2, 11, 0, 2, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 8, 3, 2,
11, 8, 11, 9, 8, -1, -1, -1, -1, -1, -1, 3, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 10, 2,
8, 10, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 9, 0, 2, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 10,
2, 1, 9, 10, 9, 8, 10, -1, -1, -1, -1, -1, -1, 3, 11, 1, 10, 11, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0,
11, 1, 0, 8, 11, 8, 10, 11, -1, -1, -1, -1, -1, -1, 3, 9, 0, 3, 10, 9, 10, 11, 9, -1, -1, -1, -1, -1, -1, 9,
8, 11, 11, 8, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 7, 8, -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, 0, 1, 9, 8, 4, 7, -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, 2, 11, 8, 4, 7, -1, -1, -1, -1, -1, -1, -1, -1,
-1, 3, 4, 7, 3, 0, 4, 1, 2, 11, -1, -1, -1, -1, -1, -1, 9, 2, 11, 9, 0, 2, 8, 4, 7, -1, -1, -1, -1, -1, -1,
2, 11, 9, 2, 9, 7, 2, 7, 3, 7, 9, 4, -1, -1, -1, 8, 4, 7, 3, 10, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10,
4, 7, 10, 2, 4, 2, 0, 4, -1, -1, -1, -1, -1, -1, 9, 0, 1, 8, 4, 7, 2, 3, 10, -1, -1, -1, -1, -1, -1, 4, 7,
10, 9, 4, 10, 9, 10, 2, 9, 2, 1, -1, -1, -1, 3, 11, 1, 3, 10, 11, 7, 8, 4, -1, -1, -1, -1, -1, -1, 1, 10,
11, 1, 4, 10, 1, 0, 4, 7, 10, 4, -1, -1, -1, 4, 7, 8, 9, 0, 10, 9, 10, 11, 10, 0, 3, -1, -1, -1, 4, 7, 10,
4, 10, 9, 9, 10, 11, -1, -1, -1, -1, -1, -1, 9, 5, 4, -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, 0, 5, 4, 1, 5, 0, -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, 2, 11, 9, 5, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 8,
1, 2, 11, 4, 9, 5, -1, -1, -1, -1, -1, -1, 5, 2, 11, 5, 4, 2, 4, 0, 2, -1, -1, -1, -1, -1, -1, 2, 11, 5, 3,
2, 5, 3, 5, 4, 3, 4, 8, -1, -1, -1, 9, 5, 4, 2, 3, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 10, 2, 0, 8,
10, 4, 9, 5, -1, -1, -1, -1, -1, -1, 0, 5, 4, 0, 1, 5, 2, 3, 10, -1, -1, -1, -1, -1, -1, 2, 1, 5, 2, 5, 8,
2, 8, 10, 4, 8, 5, -1, -1, -1, 11, 3, 10, 11, 1, 3, 9, 5, 4, -1, -1, -1, -1, -1, -1, 4, 9, 5, 0, 8, 1, 8,
11, 1, 8, 10, 11, -1, -1, -1, 5, 4, 0, 5, 0, 10, 5, 10, 11, 10, 0, 3, -1, -1, -1, 5, 4, 8, 5, 8, 11, 11, 8,
10, -1, -1, -1, -1, -1, -1, 9, 7, 8, 5, 7, 9, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 3, 0, 9, 5, 3, 5, 7, 3,
-1, -1, -1, -1, -1, -1, 0, 7, 8, 0, 1, 7, 1, 5, 7, -1, -1, -1, -1, -1, -1, 1, 5, 3, 3, 5, 7, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 9, 7, 8, 9, 5, 7, 11, 1, 2, -1, -1, -1, -1, -1, -1, 11, 1, 2, 9, 5, 0, 5, 3, 0, 5, 7, 3,
-1, -1, -1, 8, 0, 2, 8, 2, 5, 8, 5, 7, 11, 5, 2, -1, -1, -1, 2, 11, 5, 2, 5, 3, 3, 5, 7, -1, -1, -1, -1, -1,
-1, 7, 9, 5, 7, 8, 9, 3, 10, 2, -1, -1, -1, -1, -1, -1, 9, 5, 7, 9, 7, 2, 9, 2, 0, 2, 7, 10, -1, -1, -1, 2,
3, 10, 0, 1, 8, 1, 7, 8, 1, 5, 7, -1, -1, -1, 10, 2, 1, 10, 1, 7, 7, 1, 5, -1, -1, -1, -1, -1, -1, 9, 5, 8,
8, 5, 7, 11, 1, 3, 11, 3, 10, -1, -1, -1, 5, 7, 0, 5, 0, 9, 7, 10, 0, 1, 0, 11, 10, 11, 0, 10, 11, 0, 10, 0,
3, 11, 5, 0, 8, 0, 7, 5, 7, 0, 10, 11, 5, 7, 10, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 11, 6, 5, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 3, 5, 11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 0, 1, 5,
11, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 8, 3, 1, 9, 8, 5, 11, 6, -1, -1, -1, -1, -1, -1, 1, 6, 5, 2,
6, 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, 9, 6, 5, 9, 0,
6, 0, 2, 6, -1, -1, -1, -1, -1, -1, 5, 9, 8, 5, 8, 2, 5, 2, 6, 3, 2, 8, -1, -1, -1, 2, 3, 10, 11, 6, 5, -1,
-1, -1, -1, -1, -1, -1, -1, -1, 10, 0, 8, 10, 2, 0, 11, 6, 5, -1, -1, -1, -1, -1, -1, 0, 1, 9, 2, 3, 10, 5,
11, 6, -1, -1, -1, -1, -1, -1, 5, 11, 6, 1, 9, 2, 9, 10, 2, 9, 8, 10, -1, -1, -1, 6, 3, 10, 6, 5, 3, 5, 1,
3, -1, -1, -1, -1, -1, -1, 0, 8, 10, 0, 10, 5, 0, 5, 1, 5, 10, 6, -1, -1, -1, 3, 10, 6, 0, 3, 6, 0, 6, 5, 0,
5, 9, -1, -1, -1, 6, 5, 9, 6, 9, 10, 10, 9, 8, -1, -1, -1, -1, -1, -1, 5, 11, 6, 4, 7, 8, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 4, 3, 0, 4, 7, 3, 6, 5, 11, -1, -1, -1, -1, -1, -1, 1, 9, 0, 5, 11, 6, 8, 4, 7, -1, -1,
-1, -1, -1, -1, 11, 6, 5, 1, 9, 7, 1, 7, 3, 7, 9, 4, -1, -1, -1, 6, 1, 2, 6, 5, 1, 4, 7, 8, -1, -1, -1, -1,
-1, -1, 1, 2, 5, 5, 2, 6, 3, 0, 4, 3, 4, 7, -1, -1, -1, 8, 4, 7, 9, 0, 5, 0, 6, 5, 0, 2, 6, -1, -1, -1, 7,
3, 9, 7, 9, 4, 3, 2, 9, 5, 9, 6, 2, 6, 9, 3, 10, 2, 7, 8, 4, 11, 6, 5, -1, -1, -1, -1, -1, -1, 5, 11, 6, 4,
7, 2, 4, 2, 0, 2, 7, 10, -1, -1, -1, 0, 1, 9, 4, 7, 8, 2, 3, 10, 5, 11, 6, -1, -1, -1, 9, 2, 1, 9, 10, 2, 9,
4, 10, 7, 10, 4, 5, 11, 6, 8, 4, 7, 3, 10, 5, 3, 5, 1, 5, 10, 6, -1, -1, -1, 5, 1, 10, 5, 10, 6, 1, 0, 10,
7, 10, 4, 0, 4, 10, 0, 5, 9, 0, 6, 5, 0, 3, 6, 10, 6, 3, 8, 4, 7, 6, 5, 9, 6, 9, 10, 4, 7, 9, 7, 10, 9, -1,
-1, -1, 11, 4, 9, 6, 4, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 11, 6, 4, 9, 11, 0, 8, 3, -1, -1, -1, -1,
-1, -1, 11, 0, 1, 11, 6, 0, 6, 4, 0, -1, -1, -1, -1, -1, -1, 8, 3, 1, 8, 1, 6, 8, 6, 4, 6, 1, 11, -1, -1,
-1, 1, 4, 9, 1, 2, 4, 2, 6, 4, -1, -1, -1, -1, -1, -1, 3, 0, 8, 1, 2, 9, 2, 4, 9, 2, 6, 4, -1, -1, -1, 0, 2,
4, 4, 2, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 3, 2, 8, 2, 4, 4, 2, 6, -1, -1, -1, -1, -1, -1, 11, 4, 9,
11, 6, 4, 10, 2, 3, -1, -1, -1, -1, -1, -1, 0, 8, 2, 2, 8, 10, 4, 9, 11, 4, 11, 6, -1, -1, -1, 3, 10, 2, 0,
1, 6, 0, 6, 4, 6, 1, 11, -1, -1, -1, 6, 4, 1, 6, 1, 11, 4, 8, 1, 2, 1, 10, 8, 10, 1, 9, 6, 4, 9, 3, 6, 9, 1,
3, 10, 6, 3, -1, -1, -1, 8, 10, 1, 8, 1, 0, 10, 6, 1, 9, 1, 4, 6, 4, 1, 3, 10, 6, 3, 6, 0, 0, 6, 4, -1, -1,
-1, -1, -1, -1, 6, 4, 8, 10, 6, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 11, 6, 7, 8, 11, 8, 9, 11, -1, -1,
-1, -1, -1, -1, 0, 7, 3, 0, 11, 7, 0, 9, 11, 6, 7, 11, -1, -1, -1, 11, 6, 7, 1, 11, 7, 1, 7, 8, 1, 8, 0, -1,
-1, -1, 11, 6, 7, 11, 7, 1, 1, 7, 3, -1, -1, -1, -1, -1, -1, 1, 2, 6, 1, 6, 8, 1, 8, 9, 8, 6, 7, -1, -1, -1,
2, 6, 9, 2, 9, 1, 6, 7, 9, 0, 9, 3, 7, 3, 9, 7, 8, 0, 7, 0, 6, 6, 0, 2, -1, -1, -1, -1, -1, -1, 7, 3, 2, 6,
7, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 10, 11, 6, 8, 11, 8, 9, 8, 6, 7, -1, -1, -1, 2, 0, 7, 2, 7,
10, 0, 9, 7, 6, 7, 11, 9, 11, 7, 1, 8, 0, 1, 7, 8, 1, 11, 7, 6, 7, 11, 2, 3, 10, 10, 2, 1, 10, 1, 7, 11, 6,
1, 6, 7, 1, -1, -1, -1, 8, 9, 6, 8, 6, 7, 9, 1, 6, 10, 6, 3, 1, 3, 6, 0, 9, 1, 10, 6, 7, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 7, 8, 0, 7, 0, 6, 3, 10, 0, 10, 6, 0, -1, -1, -1, 7, 10, 6, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 7, 6, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 8, 10, 7, 6, -1, -1, -1, -1,
-1, -1, -1, -1, -1, 0, 1, 9, 10, 7, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 1, 9, 8, 3, 1, 10, 7, 6, -1,
-1, -1, -1, -1, -1, 11, 1, 2, 6, 10, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 11, 3, 0, 8, 6, 10, 7, -1,
-1, -1, -1, -1, -1, 2, 9, 0, 2, 11, 9, 6, 10, 7, -1, -1, -1, -1, -1, -1, 6, 10, 7, 2, 11, 3, 11, 8, 3, 11,
9, 8, -1, -1, -1, 7, 2, 3, 6, 2, 7, -1, -1, -1, -1, -1, -1, -1, -1, -1, 7, 0, 8, 7, 6, 0, 6, 2, 0, -1, -1,
-1, -1, -1, -1, 2, 7, 6, 2, 3, 7, 0, 1, 9, -1, -1, -1, -1, -1, -1, 1, 6, 2, 1, 8, 6, 1, 9, 8, 8, 7, 6, -1,
-1, -1, 11, 7, 6, 11, 1, 7, 1, 3, 7, -1, -1, -1, -1, -1, -1, 11, 7, 6, 1, 7, 11, 1, 8, 7, 1, 0, 8, -1, -1,
-1, 0, 3, 7, 0, 7, 11, 0, 11, 9, 6, 11, 7, -1, -1, -1, 7, 6, 11, 7, 11, 8, 8, 11, 9, -1, -1, -1, -1, -1, -1,
6, 8, 4, 10, 8, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 6, 10, 3, 0, 6, 0, 4, 6, -1, -1, -1, -1, -1, -1,
8, 6, 10, 8, 4, 6, 9, 0, 1, -1, -1, -1, -1, -1, -1, 9, 4, 6, 9, 6, 3, 9, 3, 1, 10, 3, 6, -1, -1, -1, 6, 8,
4, 6, 10, 8, 2, 11, 1, -1, -1, -1, -1, -1, -1, 1, 2, 11, 3, 0, 10, 0, 6, 10, 0, 4, 6, -1, -1, -1, 4, 10, 8,
4, 6, 10, 0, 2, 9, 2, 11, 9, -1, -1, -1, 11, 9, 3, 11, 3, 2, 9, 4, 3, 10, 3, 6, 4, 6, 3, 8, 2, 3, 8, 4, 2,
4, 6, 2, -1, -1, -1, -1, -1, -1, 0, 4, 2, 4, 6, 2, -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, 9, 4, 1, 4, 2, 2, 4, 6, -1, -1, -1, -1, -1, -1, 8, 1, 3, 8, 6, 1, 8, 4, 6, 6,
11, 1, -1, -1, -1, 11, 1, 0, 11, 0, 6, 6, 0, 4, -1, -1, -1, -1, -1, -1, 4, 6, 3, 4, 3, 8, 6, 11, 3, 0, 3, 9,
11, 9, 3, 11, 9, 4, 6, 11, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 9, 5, 7, 6, 10, -1, -1, -1, -1, -1, -1,
-1, -1, -1, 0, 8, 3, 4, 9, 5, 10, 7, 6, -1, -1, -1, -1, -1, -1, 5, 0, 1, 5, 4, 0, 7, 6, 10, -1, -1, -1, -1,
-1, -1, 10, 7, 6, 8, 3, 4, 3, 5, 4, 3, 1, 5, -1, -1, -1, 9, 5, 4, 11, 1, 2, 7, 6, 10, -1, -1, -1, -1, -1,
-1, 6, 10, 7, 1, 2, 11, 0, 8, 3, 4, 9, 5, -1, -1, -1, 7, 6, 10, 5, 4, 11, 4, 2, 11, 4, 0, 2, -1, -1, -1, 3,
4, 8, 3, 5, 4, 3, 2, 5, 11, 5, 2, 10, 7, 6, 7, 2, 3, 7, 6, 2, 5, 4, 9, -1, -1, -1, -1, -1, -1, 9, 5, 4, 0,
8, 6, 0, 6, 2, 6, 8, 7, -1, -1, -1, 3, 6, 2, 3, 7, 6, 1, 5, 0, 5, 4, 0, -1, -1, -1, 6, 2, 8, 6, 8, 7, 2, 1,
8, 4, 8, 5, 1, 5, 8, 9, 5, 4, 11, 1, 6, 1, 7, 6, 1, 3, 7, -1, -1, -1, 1, 6, 11, 1, 7, 6, 1, 0, 7, 8, 7, 0,
9, 5, 4, 4, 0, 11, 4, 11, 5, 0, 3, 11, 6, 11, 7, 3, 7, 11, 7, 6, 11, 7, 11, 8, 5, 4, 11, 4, 8, 11, -1, -1,
-1, 6, 9, 5, 6, 10, 9, 10, 8, 9, -1, -1, -1, -1, -1, -1, 3, 6, 10, 0, 6, 3, 0, 5, 6, 0, 9, 5, -1, -1, -1, 0,
10, 8, 0, 5, 10, 0, 1, 5, 5, 6, 10, -1, -1, -1, 6, 10, 3, 6, 3, 5, 5, 3, 1, -1, -1, -1, -1, -1, -1, 1, 2,
11, 9, 5, 10, 9, 10, 8, 10, 5, 6, -1, -1, -1, 0, 10, 3, 0, 6, 10, 0, 9, 6, 5, 6, 9, 1, 2, 11, 10, 8, 5, 10,
5, 6, 8, 0, 5, 11, 5, 2, 0, 2, 5, 6, 10, 3, 6, 3, 5, 2, 11, 3, 11, 5, 3, -1, -1, -1, 5, 8, 9, 5, 2, 8, 5, 6,
2, 3, 8, 2, -1, -1, -1, 9, 5, 6, 9, 6, 0, 0, 6, 2, -1, -1, -1, -1, -1, -1, 1, 5, 8, 1, 8, 0, 5, 6, 8, 3, 8,
2, 6, 2, 8, 1, 5, 6, 2, 1, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 3, 6, 1, 6, 11, 3, 8, 6, 5, 6, 9, 8, 9,
6, 11, 1, 0, 11, 0, 6, 9, 5, 0, 5, 6, 0, -1, -1, -1, 0, 3, 8, 5, 6, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1,
11, 5, 6, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 10, 5, 11, 7, 5, 10, -1, -1, -1, -1, -1, -1, -1,
-1, -1, 10, 5, 11, 10, 7, 5, 8, 3, 0, -1, -1, -1, -1, -1, -1, 5, 10, 7, 5, 11, 10, 1, 9, 0, -1, -1, -1, -1,
-1, -1, 11, 7, 5, 11, 10, 7, 9, 8, 1, 8, 3, 1, -1, -1, -1, 10, 1, 2, 10, 7, 1, 7, 5, 1, -1, -1, -1, -1, -1,
-1, 0, 8, 3, 1, 2, 7, 1, 7, 5, 7, 2, 10, -1, -1, -1, 9, 7, 5, 9, 2, 7, 9, 0, 2, 2, 10, 7, -1, -1, -1, 7, 5,
2, 7, 2, 10, 5, 9, 2, 3, 2, 8, 9, 8, 2, 2, 5, 11, 2, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, 8, 2, 0, 8, 5,
2, 8, 7, 5, 11, 2, 5, -1, -1, -1, 9, 0, 1, 5, 11, 3, 5, 3, 7, 3, 11, 2, -1, -1, -1, 9, 8, 2, 9, 2, 1, 8, 7,
2, 11, 2, 5, 7, 5, 2, 1, 3, 5, 3, 7, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 0, 8, 7, 0, 7, 1, 1, 7, 5, -1,
-1, -1, -1, -1, -1, 9, 0, 3, 9, 3, 5, 5, 3, 7, -1, -1, -1, -1, -1, -1, 9, 8, 7, 5, 9, 7, -1, -1, -1, -1, -1,
-1, -1, -1, -1, 5, 8, 4, 5, 11, 8, 11, 10, 8, -1, -1, -1, -1, -1, -1, 5, 0, 4, 5, 10, 0, 5, 11, 10, 10, 3,
0, -1, -1, -1, 0, 1, 9, 8, 4, 11, 8, 11, 10, 11, 4, 5, -1, -1, -1, 11, 10, 4, 11, 4, 5, 10, 3, 4, 9, 4, 1,
3, 1, 4, 2, 5, 1, 2, 8, 5, 2, 10, 8, 4, 5, 8, -1, -1, -1, 0, 4, 10, 0, 10, 3, 4, 5, 10, 2, 10, 1, 5, 1, 10,
0, 2, 5, 0, 5, 9, 2, 10, 5, 4, 5, 8, 10, 8, 5, 9, 4, 5, 2, 10, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 5,
11, 3, 5, 2, 3, 4, 5, 3, 8, 4, -1, -1, -1, 5, 11, 2, 5, 2, 4, 4, 2, 0, -1, -1, -1, -1, -1, -1, 3, 11, 2, 3,
5, 11, 3, 8, 5, 4, 5, 8, 0, 1, 9, 5, 11, 2, 5, 2, 4, 1, 9, 2, 9, 4, 2, -1, -1, -1, 8, 4, 5, 8, 5, 3, 3, 5,
1, -1, -1, -1, -1, -1, -1, 0, 4, 5, 1, 0, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, 8, 4, 5, 8, 5, 3, 9, 0, 5,
0, 3, 5, -1, -1, -1, 9, 4, 5, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 10, 7, 4, 9, 10, 9, 11, 10,
-1, -1, -1, -1, -1, -1, 0, 8, 3, 4, 9, 7, 9, 10, 7, 9, 11, 10, -1, -1, -1, 1, 11, 10, 1, 10, 4, 1, 4, 0, 7,
4, 10, -1, -1, -1, 3, 1, 4, 3, 4, 8, 1, 11, 4, 7, 4, 10, 11, 10, 4, 4, 10, 7, 9, 10, 4, 9, 2, 10, 9, 1, 2,
-1, -1, -1, 9, 7, 4, 9, 10, 7, 9, 1, 10, 2, 10, 1, 0, 8, 3, 10, 7, 4, 10, 4, 2, 2, 4, 0, -1, -1, -1, -1, -1,
-1, 10, 7, 4, 10, 4, 2, 8, 3, 4, 3, 2, 4, -1, -1, -1, 2, 9, 11, 2, 7, 9, 2, 3, 7, 7, 4, 9, -1, -1, -1, 9,
11, 7, 9, 7, 4, 11, 2, 7, 8, 7, 0, 2, 0, 7, 3, 7, 11, 3, 11, 2, 7, 4, 11, 1, 11, 0, 4, 0, 11, 1, 11, 2, 8,
7, 4, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 9, 1, 4, 1, 7, 7, 1, 3, -1, -1, -1, -1, -1, -1, 4, 9, 1, 4, 1,
7, 0, 8, 1, 8, 7, 1, -1, -1, -1, 4, 0, 3, 7, 4, 3, -1, -1, -1, -1, -1, -1, -1, -1, -1, 4, 8, 7, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, 9, 11, 8, 11, 10, 8, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 0, 9, 3, 9,
10, 10, 9, 11, -1, -1, -1, -1, -1, -1, 0, 1, 11, 0, 11, 8, 8, 11, 10, -1, -1, -1, -1, -1, -1, 3, 1, 11, 10,
3, 11, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 2, 10, 1, 10, 9, 9, 10, 8, -1, -1, -1, -1, -1, -1, 3, 0, 9, 3,
9, 10, 1, 2, 9, 2, 10, 9, -1, -1, -1, 0, 2, 10, 8, 0, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, 3, 2, 10, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 8, 2, 8, 11, 11, 8, 9, -1, -1, -1, -1, -1, -1, 9, 11, 2,
0, 9, 2, -1, -1, -1, -1, -1, -1, -1, -1, -1, 2, 3, 8, 2, 8, 11, 0, 1, 8, 1, 11, 8, -1, -1, -1, 1, 11, 2, -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, 0, 9, 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 };
}
}