Skip to content

Instantly share code, notes, and snippets.

@tiger-tiger

tiger-tiger/gist:711c16c4cd5b6c65d0000fd0fab8de3f

Forked from michalspondr/gist:54ecf97953853e10b792
Created November 16, 2021 12:29
Show Gist options
  • Save tiger-tiger/711c16c4cd5b6c65d0000fd0fab8de3f to your computer and use it in GitHub Desktop.
Save tiger-tiger/711c16c4cd5b6c65d0000fd0fab8de3f to your computer and use it in GitHub Desktop.
Download ZIP
Marching Cubes
Raw
gistfile1.c
//
// Marching Cubes Example Program
// by Cory Bloyd ([email protected])
//
// 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.
//
// gcc marchingsource.cpp -lGL -lGLU -lglut -lm
#include "stdio.h"
#include "math.h"
//This program requires the OpenGL and GLUT libraries
// You can obtain them for free from http://www.opengl.org
#include "GL/glut.h"
struct GLvector
{
GLfloat fX;
GLfloat fY;
GLfloat fZ;
};
//These tables are used so that everything can be done in little loops that you can look at all at once
// rather than in pages and pages of unrolled code.
//a2fVertexOffset lists the positions, relative to vertex0, of each of the 8 vertices of a cube
static const GLfloat a2fVertexOffset[8][3] =
{
{0.0, 0.0, 0.0},{1.0, 0.0, 0.0},{1.0, 1.0, 0.0},{0.0, 1.0, 0.0},
{0.0, 0.0, 1.0},{1.0, 0.0, 1.0},{1.0, 1.0, 1.0},{0.0, 1.0, 1.0}
};
//a2iEdgeConnection lists the index of the endpoint vertices for each of the 12 edges of the cube
static const GLint a2iEdgeConnection[12][2] =
{
{0,1}, {1,2}, {2,3}, {3,0},
{4,5}, {5,6}, {6,7}, {7,4},
{0,4}, {1,5}, {2,6}, {3,7}
};
//a2fEdgeDirection lists the direction vector (vertex1-vertex0) for each edge in the cube
static const GLfloat a2fEdgeDirection[12][3] =
{
{1.0, 0.0, 0.0},{0.0, 1.0, 0.0},{-1.0, 0.0, 0.0},{0.0, -1.0, 0.0},
{1.0, 0.0, 0.0},{0.0, 1.0, 0.0},{-1.0, 0.0, 0.0},{0.0, -1.0, 0.0},
{0.0, 0.0, 1.0},{0.0, 0.0, 1.0},{ 0.0, 0.0, 1.0},{0.0, 0.0, 1.0}
};
//a2iTetrahedronEdgeConnection lists the index of the endpoint vertices for each of the 6 edges of the tetrahedron
static const GLint a2iTetrahedronEdgeConnection[6][2] =
{
{0,1}, {1,2}, {2,0}, {0,3}, {1,3}, {2,3}
};
//a2iTetrahedronEdgeConnection lists the index of verticies from a cube
// that made up each of the six tetrahedrons within the cube
static const GLint a2iTetrahedronsInACube[6][4] =
{
{0,5,1,6},
{0,1,2,6},
{0,2,3,6},
{0,3,7,6},
{0,7,4,6},
{0,4,5,6},
};
static const GLfloat afAmbientWhite [] = {0.25, 0.25, 0.25, 1.00};
static const GLfloat afAmbientRed [] = {0.25, 0.00, 0.00, 1.00};
static const GLfloat afAmbientGreen [] = {0.00, 0.25, 0.00, 1.00};
static const GLfloat afAmbientBlue [] = {0.00, 0.00, 0.25, 1.00};
static const GLfloat afDiffuseWhite [] = {0.75, 0.75, 0.75, 1.00};
static const GLfloat afDiffuseRed [] = {0.75, 0.00, 0.00, 1.00};
static const GLfloat afDiffuseGreen [] = {0.00, 0.75, 0.00, 1.00};
static const GLfloat afDiffuseBlue [] = {0.00, 0.00, 0.75, 1.00};
static const GLfloat afSpecularWhite[] = {1.00, 1.00, 1.00, 1.00};
static const GLfloat afSpecularRed [] = {1.00, 0.25, 0.25, 1.00};
static const GLfloat afSpecularGreen[] = {0.25, 1.00, 0.25, 1.00};
static const GLfloat afSpecularBlue [] = {0.25, 0.25, 1.00, 1.00};
GLenum ePolygonMode = GL_FILL;
GLint iDataSetSize = 16;
GLfloat fStepSize = 1.0/iDataSetSize;
GLfloat fTargetValue = 48.0;
GLfloat fTime = 0.0;
GLvector sSourcePoint[3];
GLboolean bSpin = true;
GLboolean bMove = true;
GLboolean bLight = true;
void vIdle();
void vDrawScene();
void vResize(GLsizei, GLsizei);
void vKeyboard(unsigned char cKey, int iX, int iY);
void vSpecial(int iKey, int iX, int iY);
GLvoid vPrintHelp();
GLvoid vSetTime(GLfloat fTime);
GLfloat fSample1(GLfloat fX, GLfloat fY, GLfloat fZ);
GLfloat fSample2(GLfloat fX, GLfloat fY, GLfloat fZ);
GLfloat fSample3(GLfloat fX, GLfloat fY, GLfloat fZ);
GLfloat (*fSample)(GLfloat fX, GLfloat fY, GLfloat fZ) = fSample1;
GLvoid vMarchingCubes();
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale);
GLvoid vMarchCube2(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale);
GLvoid (*vMarchCube)(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale) = vMarchCube1;
int main(int argc, char **argv)
{
GLfloat afPropertiesAmbient [] = {0.50, 0.50, 0.50, 1.00};
GLfloat afPropertiesDiffuse [] = {0.75, 0.75, 0.75, 1.00};
GLfloat afPropertiesSpecular[] = {1.00, 1.00, 1.00, 1.00};
GLsizei iWidth = 640.0;
GLsizei iHeight = 480.0;
glutInit(&argc, argv);
glutInitWindowPosition( 0, 0);
glutInitWindowSize(iWidth, iHeight);
glutInitDisplayMode( GLUT_RGB | GLUT_DEPTH | GLUT_DOUBLE );
glutCreateWindow( "Marching Cubes" );
glutDisplayFunc( vDrawScene );
glutIdleFunc( vIdle );
glutReshapeFunc( vResize );
glutKeyboardFunc( vKeyboard );
glutSpecialFunc( vSpecial );
glClearColor( 0.0, 0.0, 0.0, 1.0 );
glClearDepth( 1.0 );
glEnable(GL_DEPTH_TEST);
glEnable(GL_LIGHTING);
glPolygonMode(GL_FRONT_AND_BACK, ePolygonMode);
glLightfv( GL_LIGHT0, GL_AMBIENT, afPropertiesAmbient);
glLightfv( GL_LIGHT0, GL_DIFFUSE, afPropertiesDiffuse);
glLightfv( GL_LIGHT0, GL_SPECULAR, afPropertiesSpecular);
glLightModelf(GL_LIGHT_MODEL_TWO_SIDE, 1.0);
glEnable( GL_LIGHT0 );
glMaterialfv(GL_BACK, GL_AMBIENT, afAmbientGreen);
glMaterialfv(GL_BACK, GL_DIFFUSE, afDiffuseGreen);
glMaterialfv(GL_FRONT, GL_AMBIENT, afAmbientBlue);
glMaterialfv(GL_FRONT, GL_DIFFUSE, afDiffuseBlue);
glMaterialfv(GL_FRONT, GL_SPECULAR, afSpecularWhite);
glMaterialf( GL_FRONT, GL_SHININESS, 25.0);
vResize(iWidth, iHeight);
vPrintHelp();
glutMainLoop();
}
GLvoid vPrintHelp()
{
printf("Marching Cubes Example by Cory Bloyd ([email protected])\n\n");
printf("+/- increase/decrease sample density\n");
printf("PageUp/PageDown increase/decrease surface value\n");
printf("s change sample function\n");
printf("c toggle marching cubes / marching tetrahedrons\n");
printf("w wireframe on/off\n");
printf("l toggle lighting / color-by-normal\n");
printf("Home spin scene on/off\n");
printf("End source point animation on/off\n");
}
void vResize( GLsizei iWidth, GLsizei iHeight )
{
GLfloat fAspect, fHalfWorldSize = (1.4142135623730950488016887242097/2);
glViewport( 0, 0, iWidth, iHeight );
glMatrixMode (GL_PROJECTION);
glLoadIdentity ();
if(iWidth <= iHeight)
{
fAspect = (GLfloat)iHeight / (GLfloat)iWidth;
glOrtho(-fHalfWorldSize, fHalfWorldSize, -fHalfWorldSize*fAspect,
fHalfWorldSize*fAspect, -10*fHalfWorldSize, 10*fHalfWorldSize);
}
else
{
fAspect = (GLfloat)iWidth / (GLfloat)iHeight;
glOrtho(-fHalfWorldSize*fAspect, fHalfWorldSize*fAspect, -fHalfWorldSize,
fHalfWorldSize, -10*fHalfWorldSize, 10*fHalfWorldSize);
}
glMatrixMode( GL_MODELVIEW );
}
void vKeyboard(unsigned char cKey, int iX, int iY)
{
switch(cKey)
{
case 'w' :
{
if(ePolygonMode == GL_LINE)
{
ePolygonMode = GL_FILL;
}
else
{
ePolygonMode = GL_LINE;
}
glPolygonMode(GL_FRONT_AND_BACK, ePolygonMode);
} break;
case '+' :
case '=' :
{
++iDataSetSize;
fStepSize = 1.0/iDataSetSize;
} break;
case '-' :
{
if(iDataSetSize > 1)
{
--iDataSetSize;
fStepSize = 1.0/iDataSetSize;
}
} break;
case 'c' :
{
if(vMarchCube == vMarchCube1)
{
vMarchCube = vMarchCube2;//Use Marching Tetrahedrons
}
else
{
vMarchCube = vMarchCube1;//Use Marching Cubes
}
} break;
case 's' :
{
if(fSample == fSample1)
{
fSample = fSample2;
}
else if(fSample == fSample2)
{
fSample = fSample3;
}
else
{
fSample = fSample1;
}
} break;
case 'l' :
{
if(bLight)
{
glDisable(GL_LIGHTING);//use vertex colors
}
else
{
glEnable(GL_LIGHTING);//use lit material color
}
bLight = !bLight;
};
}
}
void vSpecial(int iKey, int iX, int iY)
{
switch(iKey)
{
case GLUT_KEY_PAGE_UP :
{
if(fTargetValue < 1000.0)
{
fTargetValue *= 1.1;
}
} break;
case GLUT_KEY_PAGE_DOWN :
{
if(fTargetValue > 1.0)
{
fTargetValue /= 1.1;
}
} break;
case GLUT_KEY_HOME :
{
bSpin = !bSpin;
} break;
case GLUT_KEY_END :
{
bMove = !bMove;
} break;
}
}
void vIdle()
{
glutPostRedisplay();
}
void vDrawScene()
{
static GLfloat fPitch = 0.0;
static GLfloat fYaw = 0.0;
static GLfloat fTime = 0.0;
glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT );
glPushMatrix();
if(bSpin)
{
fPitch += 4.0;
fYaw += 2.5;
}
if(bMove)
{
fTime += 0.025;
}
vSetTime(fTime);
glTranslatef(0.0, 0.0, -1.0);
glRotatef( -fPitch, 1.0, 0.0, 0.0);
glRotatef( 0.0, 0.0, 1.0, 0.0);
glRotatef( fYaw, 0.0, 0.0, 1.0);
glPushAttrib(GL_LIGHTING_BIT);
glDisable(GL_LIGHTING);
glColor3f(1.0, 1.0, 1.0);
glutWireCube(1.0);
glPopAttrib();
glPushMatrix();
glTranslatef(-0.5, -0.5, -0.5);
glBegin(GL_TRIANGLES);
vMarchingCubes();
glEnd();
glPopMatrix();
glPopMatrix();
glutSwapBuffers();
}
//fGetOffset finds the approximate point of intersection of the surface
// between two points with the values fValue1 and fValue2
GLfloat fGetOffset(GLfloat fValue1, GLfloat fValue2, GLfloat fValueDesired)
{
GLdouble fDelta = fValue2 - fValue1;
if(fDelta == 0.0)
{
return 0.5;
}
return (fValueDesired - fValue1)/fDelta;
}
//vGetColor generates a color from a given position and normal of a point
GLvoid vGetColor(GLvector &rfColor, GLvector &rfPosition, GLvector &rfNormal)
{
GLfloat fX = rfNormal.fX;
GLfloat fY = rfNormal.fY;
GLfloat fZ = rfNormal.fZ;
rfColor.fX = (fX > 0.0 ? fX : 0.0) + (fY < 0.0 ? -0.5*fY : 0.0) + (fZ < 0.0 ? -0.5*fZ : 0.0);
rfColor.fY = (fY > 0.0 ? fY : 0.0) + (fZ < 0.0 ? -0.5*fZ : 0.0) + (fX < 0.0 ? -0.5*fX : 0.0);
rfColor.fZ = (fZ > 0.0 ? fZ : 0.0) + (fX < 0.0 ? -0.5*fX : 0.0) + (fY < 0.0 ? -0.5*fY : 0.0);
}
GLvoid vNormalizeVector(GLvector &rfVectorResult, GLvector &rfVectorSource)
{
GLfloat fOldLength;
GLfloat fScale;
fOldLength = sqrtf( (rfVectorSource.fX * rfVectorSource.fX) +
(rfVectorSource.fY * rfVectorSource.fY) +
(rfVectorSource.fZ * rfVectorSource.fZ) );
if(fOldLength == 0.0)
{
rfVectorResult.fX = rfVectorSource.fX;
rfVectorResult.fY = rfVectorSource.fY;
rfVectorResult.fZ = rfVectorSource.fZ;
}
else
{
fScale = 1.0/fOldLength;
rfVectorResult.fX = rfVectorSource.fX*fScale;
rfVectorResult.fY = rfVectorSource.fY*fScale;
rfVectorResult.fZ = rfVectorSource.fZ*fScale;
}
}
//Generate a sample data set. fSample1(), fSample2() and fSample3() define three scalar fields whose
// values vary by the X,Y and Z coordinates and by the fTime value set by vSetTime()
GLvoid vSetTime(GLfloat fNewTime)
{
GLfloat fOffset;
GLint iSourceNum;
for(iSourceNum = 0; iSourceNum < 3; iSourceNum++)
{
sSourcePoint[iSourceNum].fX = 0.5;
sSourcePoint[iSourceNum].fY = 0.5;
sSourcePoint[iSourceNum].fZ = 0.5;
}
fTime = fNewTime;
fOffset = 1.0 + sinf(fTime);
sSourcePoint[0].fX *= fOffset;
sSourcePoint[1].fY *= fOffset;
sSourcePoint[2].fZ *= fOffset;
}
//fSample1 finds the distance of (fX, fY, fZ) from three moving points
GLfloat fSample1(GLfloat fX, GLfloat fY, GLfloat fZ)
{
GLdouble fResult = 0.0;
GLdouble fDx, fDy, fDz;
fDx = fX - sSourcePoint[0].fX;
fDy = fY - sSourcePoint[0].fY;
fDz = fZ - sSourcePoint[0].fZ;
fResult += 0.5/(fDx*fDx + fDy*fDy + fDz*fDz);
fDx = fX - sSourcePoint[1].fX;
fDy = fY - sSourcePoint[1].fY;
fDz = fZ - sSourcePoint[1].fZ;
fResult += 1.0/(fDx*fDx + fDy*fDy + fDz*fDz);
fDx = fX - sSourcePoint[2].fX;
fDy = fY - sSourcePoint[2].fY;
fDz = fZ - sSourcePoint[2].fZ;
fResult += 1.5/(fDx*fDx + fDy*fDy + fDz*fDz);
return fResult;
}
//fSample2 finds the distance of (fX, fY, fZ) from three moving lines
GLfloat fSample2(GLfloat fX, GLfloat fY, GLfloat fZ)
{
GLdouble fResult = 0.0;
GLdouble fDx, fDy, fDz;
fDx = fX - sSourcePoint[0].fX;
fDy = fY - sSourcePoint[0].fY;
fResult += 0.5/(fDx*fDx + fDy*fDy);
fDx = fX - sSourcePoint[1].fX;
fDz = fZ - sSourcePoint[1].fZ;
fResult += 0.75/(fDx*fDx + fDz*fDz);
fDy = fY - sSourcePoint[2].fY;
fDz = fZ - sSourcePoint[2].fZ;
fResult += 1.0/(fDy*fDy + fDz*fDz);
return fResult;
}
//fSample2 defines a height field by plugging the distance from the center into the sin and cos functions
GLfloat fSample3(GLfloat fX, GLfloat fY, GLfloat fZ)
{
GLfloat fHeight = 20.0*(fTime + sqrt((0.5-fX)*(0.5-fX) + (0.5-fY)*(0.5-fY)));
fHeight = 1.5 + 0.1*(sinf(fHeight) + cosf(fHeight));
GLdouble fResult = (fHeight - fZ)*50.0;
return fResult;
}
//vGetNormal() finds the gradient of the scalar field at a point
//This gradient can be used as a very accurate vertx normal for lighting calculations
GLvoid vGetNormal(GLvector &rfNormal, GLfloat fX, GLfloat fY, GLfloat fZ)
{
rfNormal.fX = fSample(fX-0.01, fY, fZ) - fSample(fX+0.01, fY, fZ);
rfNormal.fY = fSample(fX, fY-0.01, fZ) - fSample(fX, fY+0.01, fZ);
rfNormal.fZ = fSample(fX, fY, fZ-0.01) - fSample(fX, fY, fZ+0.01);
vNormalizeVector(rfNormal, rfNormal);
}
//vMarchCube1 performs the Marching Cubes algorithm on a single cube
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale)
{
extern GLint aiCubeEdgeFlags[256];
extern GLint a2iTriangleConnectionTable[256][16];
GLint iCorner, iVertex, iVertexTest, iEdge, iTriangle, iFlagIndex, iEdgeFlags;
GLfloat fOffset;
GLvector sColor;
GLfloat afCubeValue[8];
GLvector asEdgeVertex[12];
GLvector asEdgeNorm[12];
//Make a local copy of the values at the cube's corners
for(iVertex = 0; iVertex < 8; iVertex++)
{
afCubeValue[iVertex] = fSample(fX + a2fVertexOffset[iVertex][0]*fScale,
fY + a2fVertexOffset[iVertex][1]*fScale,
fZ + a2fVertexOffset[iVertex][2]*fScale);
}
//Find which vertices are inside of the surface and which are outside
iFlagIndex = 0;
for(iVertexTest = 0; iVertexTest < 8; iVertexTest++)
{
if(afCubeValue[iVertexTest] <= fTargetValue)
iFlagIndex |= 1<<iVertexTest;
}
//Find which edges are intersected by the surface
iEdgeFlags = aiCubeEdgeFlags[iFlagIndex];
//If the cube is entirely inside or outside of the surface, then there will be no intersections
if(iEdgeFlags == 0)
{
return;
}
//Find the point of intersection of the surface with each edge
//Then find the normal to the surface at those points
for(iEdge = 0; iEdge < 12; iEdge++)
{
//if there is an intersection on this edge
if(iEdgeFlags & (1<<iEdge))
{
fOffset = fGetOffset(afCubeValue[ a2iEdgeConnection[iEdge][0] ],
afCubeValue[ a2iEdgeConnection[iEdge][1] ], fTargetValue);
asEdgeVertex[iEdge].fX = fX + (a2fVertexOffset[ a2iEdgeConnection[iEdge][0] ][0] + fOffset * a2fEdgeDirection[iEdge][0]) * fScale;
asEdgeVertex[iEdge].fY = fY + (a2fVertexOffset[ a2iEdgeConnection[iEdge][0] ][1] + fOffset * a2fEdgeDirection[iEdge][1]) * fScale;
asEdgeVertex[iEdge].fZ = fZ + (a2fVertexOffset[ a2iEdgeConnection[iEdge][0] ][2] + fOffset * a2fEdgeDirection[iEdge][2]) * fScale;
vGetNormal(asEdgeNorm[iEdge], asEdgeVertex[iEdge].fX, asEdgeVertex[iEdge].fY, asEdgeVertex[iEdge].fZ);
}
}
//Draw the triangles that were found. There can be up to five per cube
for(iTriangle = 0; iTriangle < 5; iTriangle++)
{
if(a2iTriangleConnectionTable[iFlagIndex][3*iTriangle] < 0)
break;
for(iCorner = 0; iCorner < 3; iCorner++)
{
iVertex = a2iTriangleConnectionTable[iFlagIndex][3*iTriangle+iCorner];
vGetColor(sColor, asEdgeVertex[iVertex], asEdgeNorm[iVertex]);
glColor3f(sColor.fX, sColor.fY, sColor.fZ);
glNormal3f(asEdgeNorm[iVertex].fX, asEdgeNorm[iVertex].fY, asEdgeNorm[iVertex].fZ);
glVertex3f(asEdgeVertex[iVertex].fX, asEdgeVertex[iVertex].fY, asEdgeVertex[iVertex].fZ);
}
}
}
//vMarchTetrahedron performs the Marching Tetrahedrons algorithm on a single tetrahedron
GLvoid vMarchTetrahedron(GLvector *pasTetrahedronPosition, GLfloat *pafTetrahedronValue)
{
extern GLint aiTetrahedronEdgeFlags[16];
extern GLint a2iTetrahedronTriangles[16][7];
GLint iEdge, iVert0, iVert1, iEdgeFlags, iTriangle, iCorner, iVertex, iFlagIndex = 0;
GLfloat fOffset, fInvOffset, fValue = 0.0;
GLvector asEdgeVertex[6];
GLvector asEdgeNorm[6];
GLvector sColor;
//Find which vertices are inside of the surface and which are outside
for(iVertex = 0; iVertex < 4; iVertex++)
{
if(pafTetrahedronValue[iVertex] <= fTargetValue)
iFlagIndex |= 1<<iVertex;
}
//Find which edges are intersected by the surface
iEdgeFlags = aiTetrahedronEdgeFlags[iFlagIndex];
//If the tetrahedron is entirely inside or outside of the surface, then there will be no intersections
if(iEdgeFlags == 0)
{
return;
}
//Find the point of intersection of the surface with each edge
// Then find the normal to the surface at those points
for(iEdge = 0; iEdge < 6; iEdge++)
{
//if there is an intersection on this edge
if(iEdgeFlags & (1<<iEdge))
{
iVert0 = a2iTetrahedronEdgeConnection[iEdge][0];
iVert1 = a2iTetrahedronEdgeConnection[iEdge][1];
fOffset = fGetOffset(pafTetrahedronValue[iVert0], pafTetrahedronValue[iVert1], fTargetValue);
fInvOffset = 1.0 - fOffset;
asEdgeVertex[iEdge].fX = fInvOffset*pasTetrahedronPosition[iVert0].fX + fOffset*pasTetrahedronPosition[iVert1].fX;
asEdgeVertex[iEdge].fY = fInvOffset*pasTetrahedronPosition[iVert0].fY + fOffset*pasTetrahedronPosition[iVert1].fY;
asEdgeVertex[iEdge].fZ = fInvOffset*pasTetrahedronPosition[iVert0].fZ + fOffset*pasTetrahedronPosition[iVert1].fZ;
vGetNormal(asEdgeNorm[iEdge], asEdgeVertex[iEdge].fX, asEdgeVertex[iEdge].fY, asEdgeVertex[iEdge].fZ);
}
}
//Draw the triangles that were found. There can be up to 2 per tetrahedron
for(iTriangle = 0; iTriangle < 2; iTriangle++)
{
if(a2iTetrahedronTriangles[iFlagIndex][3*iTriangle] < 0)
break;
for(iCorner = 0; iCorner < 3; iCorner++)
{
iVertex = a2iTetrahedronTriangles[iFlagIndex][3*iTriangle+iCorner];
vGetColor(sColor, asEdgeVertex[iVertex], asEdgeNorm[iVertex]);
glColor3f(sColor.fX, sColor.fY, sColor.fZ);
glNormal3f(asEdgeNorm[iVertex].fX, asEdgeNorm[iVertex].fY, asEdgeNorm[iVertex].fZ);
glVertex3f(asEdgeVertex[iVertex].fX, asEdgeVertex[iVertex].fY, asEdgeVertex[iVertex].fZ);
}
}
}
//vMarchCube2 performs the Marching Tetrahedrons algorithm on a single cube by making six calls to vMarchTetrahedron
GLvoid vMarchCube2(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale)
{
GLint iVertex, iTetrahedron, iVertexInACube;
GLvector asCubePosition[8];
GLfloat afCubeValue[8];
GLvector asTetrahedronPosition[4];
GLfloat afTetrahedronValue[4];
//Make a local copy of the cube's corner positions
for(iVertex = 0; iVertex < 8; iVertex++)
{
asCubePosition[iVertex].fX = fX + a2fVertexOffset[iVertex][0]*fScale;
asCubePosition[iVertex].fY = fY + a2fVertexOffset[iVertex][1]*fScale;
asCubePosition[iVertex].fZ = fZ + a2fVertexOffset[iVertex][2]*fScale;
}
//Make a local copy of the cube's corner values
for(iVertex = 0; iVertex < 8; iVertex++)
{
afCubeValue[iVertex] = fSample(asCubePosition[iVertex].fX,
asCubePosition[iVertex].fY,
asCubePosition[iVertex].fZ);
}
for(iTetrahedron = 0; iTetrahedron < 6; iTetrahedron++)
{
for(iVertex = 0; iVertex < 4; iVertex++)
{
iVertexInACube = a2iTetrahedronsInACube[iTetrahedron][iVertex];
asTetrahedronPosition[iVertex].fX = asCubePosition[iVertexInACube].fX;
asTetrahedronPosition[iVertex].fY = asCubePosition[iVertexInACube].fY;
asTetrahedronPosition[iVertex].fZ = asCubePosition[iVertexInACube].fZ;
afTetrahedronValue[iVertex] = afCubeValue[iVertexInACube];
}
vMarchTetrahedron(asTetrahedronPosition, afTetrahedronValue);
}
}
//vMarchingCubes iterates over the entire dataset, calling vMarchCube on each cube
GLvoid vMarchingCubes()
{
GLint iX, iY, iZ;
for(iX = 0; iX < iDataSetSize; iX++)
for(iY = 0; iY < iDataSetSize; iY++)
for(iZ = 0; iZ < iDataSetSize; iZ++)
{
vMarchCube(iX*fStepSize, iY*fStepSize, iZ*fStepSize, fStepSize);
}
}
// For any edge, if one vertex is inside of the surface and the other is outside of the surface
// then the edge intersects the surface
// For each of the 4 vertices of the tetrahedron can be two possible states : either inside or outside of the surface
// For any tetrahedron the are 2^4=16 possible sets of vertex states
// This table lists the edges intersected by the surface for all 16 possible vertex states
// There are 6 edges. For each entry in the table, if edge #n is intersected, then bit #n is set to 1
GLint aiTetrahedronEdgeFlags[16]=
{
0x00, 0x0d, 0x13, 0x1e, 0x26, 0x2b, 0x35, 0x38, 0x38, 0x35, 0x2b, 0x26, 0x1e, 0x13, 0x0d, 0x00,
};
// For each of the possible vertex states listed in aiTetrahedronEdgeFlags there is a specific triangulation
// of the edge intersection points. a2iTetrahedronTriangles lists all of them in the form of
// 0-2 edge triples with the list terminated by the invalid value -1.
//
// I generated this table by hand
GLint a2iTetrahedronTriangles[16][7] =
{
{-1, -1, -1, -1, -1, -1, -1},
{ 0, 3, 2, -1, -1, -1, -1},
{ 0, 1, 4, -1, -1, -1, -1},
{ 1, 4, 2, 2, 4, 3, -1},
{ 1, 2, 5, -1, -1, -1, -1},
{ 0, 3, 5, 0, 5, 1, -1},
{ 0, 2, 5, 0, 5, 4, -1},
{ 5, 4, 3, -1, -1, -1, -1},
{ 3, 4, 5, -1, -1, -1, -1},
{ 4, 5, 0, 5, 2, 0, -1},
{ 1, 5, 0, 5, 3, 0, -1},
{ 5, 2, 1, -1, -1, -1, -1},
{ 3, 4, 2, 2, 4, 1, -1},
{ 4, 1, 0, -1, -1, -1, -1},
{ 2, 3, 0, -1, -1, -1, -1},
{-1, -1, -1, -1, -1, -1, -1},
};
// For any edge, if one vertex is inside of the surface and the other is outside of the surface
// then the edge intersects the surface
// For each of the 8 vertices of the cube can be two possible states : either inside or outside of the surface
// For any cube the are 2^8=256 possible sets of vertex states
// This table lists the edges intersected by the surface for all 256 possible vertex states
// There are 12 edges. For each entry in the table, if edge #n is intersected, then bit #n is set to 1
GLint aiCubeEdgeFlags[256]=
{
0x000, 0x109, 0x203, 0x30a, 0x406, 0x50f, 0x605, 0x70c, 0x80c, 0x905, 0xa0f, 0xb06, 0xc0a, 0xd03, 0xe09, 0xf00,
0x190, 0x099, 0x393, 0x29a, 0x596, 0x49f, 0x795, 0x69c, 0x99c, 0x895, 0xb9f, 0xa96, 0xd9a, 0xc93, 0xf99, 0xe90,
0x230, 0x339, 0x033, 0x13a, 0x636, 0x73f, 0x435, 0x53c, 0xa3c, 0xb35, 0x83f, 0x936, 0xe3a, 0xf33, 0xc39, 0xd30,
0x3a0, 0x2a9, 0x1a3, 0x0aa, 0x7a6, 0x6af, 0x5a5, 0x4ac, 0xbac, 0xaa5, 0x9af, 0x8a6, 0xfaa, 0xea3, 0xda9, 0xca0,
0x460, 0x569, 0x663, 0x76a, 0x066, 0x16f, 0x265, 0x36c, 0xc6c, 0xd65, 0xe6f, 0xf66, 0x86a, 0x963, 0xa69, 0xb60,
0x5f0, 0x4f9, 0x7f3, 0x6fa, 0x1f6, 0x0ff, 0x3f5, 0x2fc, 0xdfc, 0xcf5, 0xfff, 0xef6, 0x9fa, 0x8f3, 0xbf9, 0xaf0,
0x650, 0x759, 0x453, 0x55a, 0x256, 0x35f, 0x055, 0x15c, 0xe5c, 0xf55, 0xc5f, 0xd56, 0xa5a, 0xb53, 0x859, 0x950,
0x7c0, 0x6c9, 0x5c3, 0x4ca, 0x3c6, 0x2cf, 0x1c5, 0x0cc, 0xfcc, 0xec5, 0xdcf, 0xcc6, 0xbca, 0xac3, 0x9c9, 0x8c0,
0x8c0, 0x9c9, 0xac3, 0xbca, 0xcc6, 0xdcf, 0xec5, 0xfcc, 0x0cc, 0x1c5, 0x2cf, 0x3c6, 0x4ca, 0x5c3, 0x6c9, 0x7c0,
0x950, 0x859, 0xb53, 0xa5a, 0xd56, 0xc5f, 0xf55, 0xe5c, 0x15c, 0x055, 0x35f, 0x256, 0x55a, 0x453, 0x759, 0x650,
0xaf0, 0xbf9, 0x8f3, 0x9fa, 0xef6, 0xfff, 0xcf5, 0xdfc, 0x2fc, 0x3f5, 0x0ff, 0x1f6, 0x6fa, 0x7f3, 0x4f9, 0x5f0,
0xb60, 0xa69, 0x963, 0x86a, 0xf66, 0xe6f, 0xd65, 0xc6c, 0x36c, 0x265, 0x16f, 0x066, 0x76a, 0x663, 0x569, 0x460,
0xca0, 0xda9, 0xea3, 0xfaa, 0x8a6, 0x9af, 0xaa5, 0xbac, 0x4ac, 0x5a5, 0x6af, 0x7a6, 0x0aa, 0x1a3, 0x2a9, 0x3a0,
0xd30, 0xc39, 0xf33, 0xe3a, 0x936, 0x83f, 0xb35, 0xa3c, 0x53c, 0x435, 0x73f, 0x636, 0x13a, 0x033, 0x339, 0x230,
0xe90, 0xf99, 0xc93, 0xd9a, 0xa96, 0xb9f, 0x895, 0x99c, 0x69c, 0x795, 0x49f, 0x596, 0x29a, 0x393, 0x099, 0x190,
0xf00, 0xe09, 0xd03, 0xc0a, 0xb06, 0xa0f, 0x905, 0x80c, 0x70c, 0x605, 0x50f, 0x406, 0x30a, 0x203, 0x109, 0x000
};
// For each of the possible vertex states listed in aiCubeEdgeFlags there is a specific triangulation
// of the edge intersection points. a2iTriangleConnectionTable lists all of them in the form of
// 0-5 edge triples with the list terminated by the invalid value -1.
// For example: a2iTriangleConnectionTable[3] list the 2 triangles formed when corner[0]
// and corner[1] are inside of the surface, but the rest of the cube is not.
//
// I found this table in an example program someone wrote long ago. It was probably generated by hand
GLint a2iTriangleConnectionTable[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}
};
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment