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Marching Cube(C++ OpenGl代码)读取医学三维图像*.raw进行三维重建-StubbornHuang Blog

2 未使用显示列表的代码

#define GLUT_DISABLE_ATEXIT_HACK 
#include <stdlib.h>
#include <string.h>
#include "stdio.h"
#include "math.h"
#include "GL/glut.h"

#if !defined(GLUT_WHEEL_UP)
#  define GLUT_WHEEL_UP   3
#  define GLUT_WHEEL_DOWN 4
#endif

//向量
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      立方体8个顶点
//  立方体8个顶点
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    立方体12个边
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    立方体 12个边的方向向量
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}
};



static const GLfloat afAmbientWhite [] = {0.25, 0.25, 0.25, 1.00};   // 周围 环绕 白
static const GLfloat afAmbientRed   [] = {0.25, 0.00, 0.00, 1.00};   // 周围 环绕 红
static const GLfloat afAmbientGreen [] = {0.00, 0.25, 0.00, 1.00};   // 周围 环绕 绿
static const GLfloat afAmbientBlue  [] = {0.00, 0.00, 0.25, 1.00};   // 周围 环绕 蓝
static const GLfloat afDiffuseWhite [] = {0.75, 0.75, 0.75, 1.00};   // 漫射 白
static const GLfloat afDiffuseRed   [] = {0.75, 0.00, 0.00, 1.00};   // 漫射 红
static const GLfloat afDiffuseGreen [] = {0.00, 0.75, 0.00, 1.00};   // 漫射 绿
static const GLfloat afDiffuseBlue  [] = {0.00, 0.00, 0.75, 1.00};   // 漫射 蓝
static const GLfloat afSpecularWhite[] = {1.00, 1.00, 1.00, 1.00};   // 反射 白
static const GLfloat afSpecularRed  [] = {1.00, 0.25, 0.25, 1.00};   // 反射 红
static const GLfloat afSpecularGreen[] = {0.25, 1.00, 0.25, 1.00};   // 反射 绿
static const GLfloat afSpecularBlue [] = {0.25, 0.25, 1.00, 1.00};   // 反射 蓝


GLenum    ePolygonMode = GL_FILL;

GLfloat   fTargetValue = 100.0;
GLfloat   fTime = 0.0;
GLvector  sSourcePoint[3];
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);



void spinDisplay();
void fYawDisplay(void);
void myMouseCall(int button, int state, int x ,int y);

GLvoid vPrintHelp();


GLvoid vMarchingCubes();
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale);

GLvoid (*vMarchCube)(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale) = vMarchCube1;

//
#define NX 200 
#define NY 160
#define NZ 160
//
//#define NX 48 
//#define NY 62
//#define NZ 42

short int ***data;
GLfloat HoriRotate  = 90;
GLfloat VertiRotate = 0;

GLfloat  Xtranform=-90.0;
GLfloat  Ytranform= 80.0;
GLfloat  Ztranform=-10.0;

GLfloat ZoonAspect=140.0;
GLfloat ZoomScale=1.0;
short int themax = 0,themin = 255;


void main(int argc, char **argv) 
{ 
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
        int i,j,k,c;
    short int isolevel = 128;

    FILE *fptr;
        argc=2;

    argv[1]="F:软件OpenGLmri.raw";

        for (i=1;i<argc;i++) {
        if (strcmp(argv[i],"-i") == 0)
            isolevel = atof(argv[i+1]);
    }

    // Malloc the volumetric data, hardwired size!
    data = (short int ***)malloc(NX*sizeof(short int **));
    for (i=0;i<NX;i++)
        data[i] = (short int **)malloc(NY*sizeof(short int *));
    for (i=0;i<NX;i++)
        for (j=0;j<NY;j++)
            data[i][j] = (short int *)malloc(NZ*sizeof(short int));

    // Open and read the raw data
    fprintf(stderr,"Reading data ...n");
    if ((fptr = fopen(argv[argc-1],"rb")) == NULL) {
        fprintf(stderr,"File open failedn");
        exit(-1);
    }
    for (k=0;k<NZ;k++) {
        for (j=0;j<NY;j++) {
            for (i=0;i<NX;i++) {
                if ((c = fgetc(fptr)) == EOF) {
                    fprintf(stderr,"Unexpected end of filen");
                    exit(-1);
                }
                data[i][j][k] = c;

                if (c > themax)
                    themax = c;
                if (c < themin)
                    themin = c;
            }
        }
    }
    fclose(fptr);
    fprintf(stderr,"Volumetric data range: %d -> %dn",themin,themax);
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

        GLfloat afPropertiesAmbient [] = {0.25, 0.25, 0.25, 1.00}; 
        GLfloat afPropertiesDiffuse [] = {0.75, 0.75, 0.75, 1.00}; 
        GLfloat afPropertiesSpecular[] = {1.00, 0.25, 0.25, 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 );
        glutMouseFunc(myMouseCall);

        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 ); 


        // 材质颜色  ***里外 ***
        glMaterialfv(GL_BACK,  GL_AMBIENT,   afAmbientRed); 
        glMaterialfv(GL_BACK,  GL_DIFFUSE,   afDiffuseRed); 
        glMaterialfv(GL_FRONT, GL_AMBIENT,   afAmbientWhite); 
        glMaterialfv(GL_FRONT, GL_DIFFUSE,   afDiffuseWhite); 
        glMaterialfv(GL_FRONT, GL_SPECULAR,  afSpecularWhite); 
        glMaterialf( GL_FRONT, GL_SHININESS, 10.0); 

        vResize(iWidth, iHeight); 

        vPrintHelp();
        glutMainLoop(); 
}

// 帮助内容
GLvoid vPrintHelp()
{
        printf("Marching Cubes Rountines by Niu Kenan (niukenan@sina.com)nn");
}

// 窗口改变响应
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*ZoonAspect, fHalfWorldSize*ZoonAspect, -fHalfWorldSize*fAspect*ZoonAspect,
                        fHalfWorldSize*fAspect*ZoonAspect, -10*fHalfWorldSize*ZoonAspect, 10*fHalfWorldSize*ZoonAspect);

         }
        else
        {
                fAspect = (GLfloat)iWidth / (GLfloat)iHeight; 
                glOrtho(-fHalfWorldSize*fAspect*ZoonAspect, fHalfWorldSize*fAspect*ZoonAspect, -fHalfWorldSize*ZoonAspect,
                        fHalfWorldSize*ZoonAspect, -10*fHalfWorldSize*ZoonAspect, 10*fHalfWorldSize*ZoonAspect);

        }
        glMatrixMode( GL_MODELVIEW );

}

void spinDisplay(void)
{
    HoriRotate = HoriRotate+10.0;
    if (HoriRotate >360.0)
        HoriRotate = HoriRotate -360.0;
    glutPostRedisplay();
}
void fYawDisplay(void)
{
    VertiRotate = VertiRotate+10.0;
    if (VertiRotate >360.0)
        VertiRotate = VertiRotate -360.0;
    glutPostRedisplay();

}

// 鼠标响应
void myMouseCall(int button, int state, int x ,int y)
{
    switch (button)
    {
    case GLUT_LEFT_BUTTON:
        if (state == GLUT_DOWN)
            spinDisplay();
        break;


    case GLUT_RIGHT_BUTTON:
        if(state == GLUT_DOWN)
            fYawDisplay();
        break;

    case GLUT_WHEEL_UP:

            ZoomScale=ZoomScale+0.05;
            glutPostRedisplay();
        break;

    case GLUT_WHEEL_DOWN:
            ZoomScale=ZoomScale-0.05;
            glutPostRedisplay();

        break;


    default:
        break;
    }
}

// 键盘响应
void vKeyboard(unsigned char cKey, int iX, int iY)
{
        switch(cKey)
        {
                case 'w' :
                {
                        if(ePolygonMode == GL_LINE)
                        {
                                ePolygonMode = GL_FILL;
                                glutPostRedisplay();
                        }
                        else
                        {
                                ePolygonMode = GL_LINE;
                                glutPostRedisplay();
                        }
                        glPolygonMode(GL_FRONT_AND_BACK, ePolygonMode);
                } break;


                case 'l' :
                {
                        if(bLight)
                        {
                                glDisable(GL_LIGHTING);//use vertex colors
                                glutPostRedisplay();
                        }
                        else
                        {
                                glEnable(GL_LIGHTING);//use lit material color
                                glutPostRedisplay();
                        }

                        bLight = !bLight;
                };
        }
}

//特殊键响应 上下左右 PaUP PaDn
void vSpecial(int iKey, int iX, int iY)
{
        switch(iKey)
        {
                case GLUT_KEY_F1 :
                {
                    ZoonAspect-=10;
                    glutReshapeFunc( vResize );

                } break;


        ////////////////////////////////////////////
                case GLUT_KEY_PAGE_UP :
                {
                    if(fTargetValue<=themax-1)
                    {
                    fTargetValue=fTargetValue+1;
                    }
                    else
                    {
                        fTargetValue=themax;
                    }
                    glutPostRedisplay();


                } break;
                case GLUT_KEY_PAGE_DOWN :
                {
                    if(fTargetValue>=themin+1)
                    {
                    fTargetValue=fTargetValue-1;
                    }
                    else
                    {
                        fTargetValue=themin;
                    }
                    glutPostRedisplay();

                } break;
////////////////////////////////////////////////////////////////////////////


//***                     键盘 上下左右 控制               ***//
///////////////////////////////////////////////////////////////////////
                case GLUT_KEY_UP :    // 上
                {
                      Ytranform+=10.0;
                      glutPostRedisplay();
                } break;

                 case GLUT_KEY_DOWN :   // 下
                {
                      Ytranform-=10.0;
                      glutPostRedisplay();
                } break;

                case GLUT_KEY_LEFT :    // 左
                {
                        Xtranform-=10.0;
                        glutPostRedisplay();
                } break;

                case GLUT_KEY_RIGHT :   //  右
                {
                        Xtranform+=10.0;
                        glutPostRedisplay();
                } break;
/////////////////////////////////////////////////////////////////////////
        }
}


void vIdle()//   程序空闲时
{
        // 重绘函数
        //glutPostRedisplay();

}

void vDrawScene() // 绘制场景
{ 

        glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); 

        glPushMatrix(); 


        glTranslatef(Xtranform, Ytranform, Ztranform); 
        /*printf("%f,  %f,  %f n" ,Xtranform, Ytranform, Ztranform );
        printf("%f,  %f n" ,VertiRotate, HoriRotate);*/
        glRotatef(     HoriRotate, 1.0, 0.0, 0.0);
        glRotatef(     0.0, 0.0, 1.0, 0.0);
        glRotatef(     VertiRotate, 0.0, 0.0, 1.0);

        glScaled(ZoomScale,ZoomScale,ZoomScale);

        glPushAttrib(GL_LIGHTING_BIT);
                glDisable(GL_LIGHTING);
               /* glColor3f(1.0, 1.0, 1.0);
                glutWireCube(100.0); */
        glPopAttrib(); 


        glBegin(GL_TRIANGLES);
                vMarchingCubes();
        glEnd();

        glPopMatrix(); 

        glutSwapBuffers(); 
}

//************************************************************************************************************************************************
/*                                                             Marching Cube 计算相关函数                                                       */
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//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;
}

// 根据 位置 以及 法向量 产生颜色    
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);
}
//向量标准化
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;
        }
}




//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)                   // 计算 数据场一点的梯度
{
      if (  fX>1 && fX<NX-1 &&    fY>1 && fY<NY-1  &&  fZ>1 && fZ<NZ-1    )
      {
        rfNormal.fX = (GLfloat)data[(int)fX-1][ (int)fY][ (int)fZ] - (GLfloat)data[(int)fX+1][ (int)fY] [(int)fZ];
        rfNormal.fY = (GLfloat)data[(int)fX] [(int)fY-1] [(int)fZ] - (GLfloat)data[(int)fX][(int) fY+1][(int)fZ];
        rfNormal.fZ = (GLfloat)data[(int)fX][(int)fY][(int) fZ-1] - (GLfloat)data[(int)fX][ (int)fY][ (int)fZ+1];
        vNormalizeVector(rfNormal, rfNormal);
      }
}

//vMarchCube1 performs the Marching Cubes algorithm on a single cube
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale)                   // Marching Cubes 算法对于一个 单个立方体
{
        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  保存 每一个Cube的八个顶点。       
        for(iVertex = 0; iVertex < 8; iVertex++)
        {
            afCubeValue[iVertex] =(GLfloat)data[(int)(fX + a2fVertexOffset[iVertex][0])]
                                                  [(int)(fY + a2fVertexOffset[iVertex][1])]
                                                 [(int)(fZ + a2fVertexOffset[iVertex][2])] ;
        }

        //Find which vertices are inside of the surface and which are outside   找出哪些顶点是在等值面内,哪些是在等值面外
        iFlagIndex = 0;
        for(iVertexTest = 0; iVertexTest < 8; iVertexTest++)
        {
                if(afCubeValue[iVertexTest] <= fTargetValue) 
                        iFlagIndex |= 1<<iVertexTest;
        }

        //Find which edges are intersected by the surface  找到与等值面有交点的 边
        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 找到每一个与等值面相交的边,并且找到等值面在这一点的法向量
        //Then find the normal to the surface at those points
        for(iEdge = 0; iEdge < 12; iEdge++)
        {
                //if there is an intersection on this edge 如果在这一个边上有交点的话
                if(iEdgeFlags & (1<<iEdge))
                {
                        fOffset = fGetOffset(afCubeValue[ a2iEdgeConnection[iEdge][0] ], 
                                                     afCubeValue[ a2iEdgeConnection[iEdge][1] ], fTargetValue);


                        //计算交点的坐标
                        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;
                       //计算交点的法向量
                        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   画出等值面三角形 每个立方体 5个三角形
        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);
                }
        }
}

//vMarchingCubes iterates over the entire dataset, calling vMarchCube on each cube
GLvoid vMarchingCubes()
{
        GLint iX, iY, iZ;
        for(iX = 0; iX < NX-1; iX++)
        for(iY = 0; iY < NY-1; iY++)
        for(iZ = 0; iZ < NZ-1; iZ++)
        {
                vMarchCube(iX, iY, iZ, 1);
        }
        printf("finish one Draw ! !n");
}

// 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}
};

3 使用显示列表的代码

#define GLUT_DISABLE_ATEXIT_HACK 
#include <stdlib.h>
#include <string.h>
#include "stdio.h"
#include "math.h"
#include <OpenGL_Freeglut/freeglut.h>

#if !defined(GLUT_WHEEL_UP)
#  define GLUT_WHEEL_UP   3
#  define GLUT_WHEEL_DOWN 4
#endif

//向量
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      立方体8个顶点
//  立方体8个顶点
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    立方体12个边
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    立方体 12个边的方向向量
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}
};



static const GLfloat afAmbientWhite [] = {0.25, 0.25, 0.25, 1.00};   // 周围 环绕 白
static const GLfloat afAmbientRed   [] = {0.25, 0.00, 0.00, 1.00};   // 周围 环绕 红
static const GLfloat afAmbientGreen [] = {0.00, 0.25, 0.00, 1.00};   // 周围 环绕 绿
static const GLfloat afAmbientBlue  [] = {0.00, 0.00, 0.25, 1.00};   // 周围 环绕 蓝
static const GLfloat afDiffuseWhite [] = {0.75, 0.75, 0.75, 1.00};   // 漫射 白
static const GLfloat afDiffuseRed   [] = {0.75, 0.00, 0.00, 1.00};   // 漫射 红
static const GLfloat afDiffuseGreen [] = {0.00, 0.75, 0.00, 1.00};   // 漫射 绿
static const GLfloat afDiffuseBlue  [] = {0.00, 0.00, 0.75, 1.00};   // 漫射 蓝
static const GLfloat afSpecularWhite[] = {1.00, 1.00, 1.00, 1.00};   // 反射 白
static const GLfloat afSpecularRed  [] = {1.00, 0.25, 0.25, 1.00};   // 反射 红
static const GLfloat afSpecularGreen[] = {0.25, 1.00, 0.25, 1.00};   // 反射 绿
static const GLfloat afSpecularBlue [] = {0.25, 0.25, 1.00, 1.00};   // 反射 蓝


GLenum    ePolygonMode = GL_FILL;

GLfloat   fTargetValue = 100.0;
GLfloat   fTime = 0.0;
GLvector  sSourcePoint[3];
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);



void spinDisplay();
void fYawDisplay(void);
void myMouseCall(int button, int state, int x ,int y);

GLvoid vPrintHelp();


GLvoid vMarchingCubes();
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale);

GLvoid (*vMarchCube)(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale) = vMarchCube1;

//
#define NX 263 
#define NY 249
#define NZ 256
//
//#define NX 48 
//#define NY 62
//#define NZ 42

short int ***data;
GLfloat HoriRotate  = 90;
GLfloat VertiRotate = 0;

GLfloat  Xtranform=-90.0;
GLfloat  Ytranform= 80.0;
GLfloat  Ztranform=-10.0;

GLfloat ZoonAspect=140.0;
GLfloat ZoomScale=1.0;
short int themax = 0,themin = 255;

GLuint marchingCube=0;

void main(int argc, char **argv) 
{ 
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
        int i,j,k,c;
    short int isolevel = 150;

    FILE *fptr;
        argc=2;

    argv[1]="C:UsersHuangWangDesktopHead_256x256x256.raw";

        for (i=1;i<argc;i++) {
        if (strcmp(argv[i],"-i") == 0)
            isolevel = atof(argv[i+1]);
    }

    // Malloc the volumetric data, hardwired size!
    data = (short int ***)malloc(NX*sizeof(short int **));
    for (i=0;i<NX;i++)
        data[i] = (short int **)malloc(NY*sizeof(short int *));
    for (i=0;i<NX;i++)
        for (j=0;j<NY;j++)
            data[i][j] = (short int *)malloc(NZ*sizeof(short int));

    // Open and read the raw data
    fprintf(stderr,"Reading data ...n");
    if ((fptr = fopen(argv[argc-1],"rb")) == NULL) {
        fprintf(stderr,"File open failedn");
        exit(-1);
    }
    for (k=0;k<NZ;k++) {
        for (j=0;j<NY;j++) {
            for (i=0;i<NX;i++) {
                if ((c = fgetc(fptr)) == EOF) {
                    fprintf(stderr,"Unexpected end of filen");
                    exit(-1);
                }
                data[i][j][k] = c;

                if (c > themax)
                    themax = c;
                if (c < themin)
                    themin = c;
            }
        }
    }
    fclose(fptr);
    fprintf(stderr,"Volumetric data range: %d -> %dn",themin,themax);
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

        GLfloat afPropertiesAmbient [] = {0.25, 0.25, 0.25, 1.00}; 
        GLfloat afPropertiesDiffuse [] = {0.75, 0.75, 0.75, 1.00}; 
        GLfloat afPropertiesSpecular[] = {1.00, 0.25, 0.25, 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 );
    //  vMarchingCubes();
        glutCreateWindow( "Marching Cubes" );

        glutDisplayFunc( vDrawScene );
        glutIdleFunc( vIdle );
        glutReshapeFunc( vResize );
        glutKeyboardFunc( vKeyboard );
        glutSpecialFunc( vSpecial );
        glutMouseFunc(myMouseCall);

        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 ); 

        // 材质颜色  ***里外 ***
        glMaterialfv(GL_BACK,  GL_AMBIENT,   afAmbientRed); 
        glMaterialfv(GL_BACK,  GL_DIFFUSE,   afDiffuseRed); 
        glMaterialfv(GL_FRONT, GL_AMBIENT,   afAmbientWhite); 
        glMaterialfv(GL_FRONT, GL_DIFFUSE,   afDiffuseWhite); 
        glMaterialfv(GL_FRONT, GL_SPECULAR,  afSpecularWhite); 
        glMaterialf( GL_FRONT, GL_SHININESS, 10.0); 

        vResize(iWidth, iHeight); 

        vPrintHelp();
        glutMainLoop(); 
}

// 帮助内容
GLvoid vPrintHelp()
{
        printf("Marching Cubes Rountines by Niu Kenan (niukenan@sina.com)nn");
}

// 窗口改变响应
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*ZoonAspect, fHalfWorldSize*ZoonAspect, -fHalfWorldSize*fAspect*ZoonAspect,
                        fHalfWorldSize*fAspect*ZoonAspect, -10*fHalfWorldSize*ZoonAspect, 10*fHalfWorldSize*ZoonAspect);

         }
        else
        {
                fAspect = (GLfloat)iWidth / (GLfloat)iHeight; 
                glOrtho(-fHalfWorldSize*fAspect*ZoonAspect, fHalfWorldSize*fAspect*ZoonAspect, -fHalfWorldSize*ZoonAspect,
                        fHalfWorldSize*ZoonAspect, -10*fHalfWorldSize*ZoonAspect, 10*fHalfWorldSize*ZoonAspect);

        }
        glMatrixMode( GL_MODELVIEW );

}

void spinDisplay(void)
{
    HoriRotate = HoriRotate+10.0;
    if (HoriRotate >360.0)
        HoriRotate = HoriRotate -360.0;
    glutPostRedisplay();
}
void fYawDisplay(void)
{
    VertiRotate = VertiRotate+10.0;
    if (VertiRotate >360.0)
        VertiRotate = VertiRotate -360.0;
    glutPostRedisplay();

}

// 鼠标响应
void myMouseCall(int button, int state, int x ,int y)
{
    switch (button)
    {
    case GLUT_LEFT_BUTTON:
        if (state == GLUT_DOWN)
            spinDisplay();
        break;


    case GLUT_RIGHT_BUTTON:
        if(state == GLUT_DOWN)
            fYawDisplay();
        break;

    case GLUT_WHEEL_UP:

            ZoomScale=ZoomScale+0.05;
            glutPostRedisplay();
        break;

    case GLUT_WHEEL_DOWN:
            ZoomScale=ZoomScale-0.05;
            glutPostRedisplay();

        break;


    default:
        break;
    }
}

// 键盘响应
void vKeyboard(unsigned char cKey, int iX, int iY)
{
        switch(cKey)
        {
                case 'w' :
                {
                        if(ePolygonMode == GL_LINE)
                        {
                                ePolygonMode = GL_FILL;
                                glutPostRedisplay();
                        }
                        else
                        {
                                ePolygonMode = GL_LINE;
                                glutPostRedisplay();
                        }
                        glPolygonMode(GL_FRONT_AND_BACK, ePolygonMode);
                } break;


                case 'l' :
                {
                        if(bLight)
                        {
                                glDisable(GL_LIGHTING);//use vertex colors
                                glutPostRedisplay();
                        }
                        else
                        {
                                glEnable(GL_LIGHTING);//use lit material color
                                glutPostRedisplay();
                        }

                        bLight = !bLight;
                };
        }
}

//特殊键响应 上下左右 PaUP PaDn
void vSpecial(int iKey, int iX, int iY)
{
        switch(iKey)
        {
                case GLUT_KEY_F1 :
                {
                    ZoonAspect-=10;
                    glutReshapeFunc( vResize );

                } break;


        ////////////////////////////////////////////
                case GLUT_KEY_PAGE_UP :
                {
                    if(fTargetValue<=themax-1)
                    {
                    fTargetValue=fTargetValue+1;
                    }
                    else
                    {
                        fTargetValue=themax;
                    }
                    glutPostRedisplay();


                } break;
                case GLUT_KEY_PAGE_DOWN :
                {
                    if(fTargetValue>=themin+1)
                    {
                    fTargetValue=fTargetValue-1;
                    }
                    else
                    {
                        fTargetValue=themin;
                    }
                    glutPostRedisplay();

                } break;
////////////////////////////////////////////////////////////////////////////


//***                     键盘 上下左右 控制               ***//
///////////////////////////////////////////////////////////////////////
                case GLUT_KEY_UP :    // 上
                {
                      Ytranform+=10.0;
                      glutPostRedisplay();
                } break;

                 case GLUT_KEY_DOWN :   // 下
                {
                      Ytranform-=10.0;
                      glutPostRedisplay();
                } break;

                case GLUT_KEY_LEFT :    // 左
                {
                        Xtranform-=10.0;
                        glutPostRedisplay();
                } break;

                case GLUT_KEY_RIGHT :   //  右
                {
                        Xtranform+=10.0;
                        glutPostRedisplay();
                } break;
/////////////////////////////////////////////////////////////////////////
        }
}


void vIdle()//   程序空闲时
{
        // 重绘函数
        //glutPostRedisplay();

}

int i=0;
void vDrawScene() // 绘制场景
{ 
        i=i+1;
        glClear( GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT ); 

        glPushMatrix(); 

        glTranslatef(Xtranform, Ytranform, Ztranform); 
        /*printf("%f,  %f,  %f n" ,Xtranform, Ytranform, Ztranform );
        printf("%f,  %f n" ,VertiRotate, HoriRotate);*/
        glRotatef(     HoriRotate, 1.0, 0.0, 0.0);
        glRotatef(     0.0, 0.0, 1.0, 0.0);
        glRotatef(     VertiRotate, 0.0, 0.0, 1.0);

        glScaled(ZoomScale,ZoomScale,ZoomScale);
        if (i==1)
        {   
            marchingCube=glGenLists(1);
            glNewList(marchingCube,GL_COMPILE);
            vMarchingCubes();
            glEndList();
            glCallList(marchingCube);
        }
        else if(i>1)
        {
            glCallList(marchingCube);
        }

        glPushAttrib(GL_LIGHTING_BIT);
                glDisable(GL_LIGHTING);
               /* glColor3f(1.0, 1.0, 1.0);
                glutWireCube(100.0); */
        glPopAttrib(); 





        glPopMatrix(); 

        glutSwapBuffers(); 
}

//************************************************************************************************************************************************
/*                                                             Marching Cube 计算相关函数                                                       */
///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
//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;
}

// 根据 位置 以及 法向量 产生颜色    
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);
}
//向量标准化
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;
        }
}




//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)                   // 计算 数据场一点的梯度
{
      if (  fX>1 && fX<NX-1 &&    fY>1 && fY<NY-1  &&  fZ>1 && fZ<NZ-1    )
      {
        rfNormal.fX = (GLfloat)data[(int)fX-1][ (int)fY][ (int)fZ] - (GLfloat)data[(int)fX+1][ (int)fY] [(int)fZ];
        rfNormal.fY = (GLfloat)data[(int)fX] [(int)fY-1] [(int)fZ] - (GLfloat)data[(int)fX][(int) fY+1][(int)fZ];
        rfNormal.fZ = (GLfloat)data[(int)fX][(int)fY][(int) fZ-1] - (GLfloat)data[(int)fX][ (int)fY][ (int)fZ+1];
        vNormalizeVector(rfNormal, rfNormal);
      }
}

//vMarchCube1 performs the Marching Cubes algorithm on a single cube
GLvoid vMarchCube1(GLfloat fX, GLfloat fY, GLfloat fZ, GLfloat fScale)                   // Marching Cubes 算法对于一个 单个立方体
{
        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  保存 每一个Cube的八个顶点。       
        for(iVertex = 0; iVertex < 8; iVertex++)
        {
            afCubeValue[iVertex] =(GLfloat)data[(int)(fX + a2fVertexOffset[iVertex][0])]
                                                  [(int)(fY + a2fVertexOffset[iVertex][1])]
                                                 [(int)(fZ + a2fVertexOffset[iVertex][2])] ;
        }

        //Find which vertices are inside of the surface and which are outside   找出哪些顶点是在等值面内,哪些是在等值面外
        iFlagIndex = 0;
        for(iVertexTest = 0; iVertexTest < 8; iVertexTest++)
        {
                if(afCubeValue[iVertexTest] <= fTargetValue) 
                        iFlagIndex |= 1<<iVertexTest;
        }

        //Find which edges are intersected by the surface  找到与等值面有交点的 边
        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 找到每一个与等值面相交的边,并且找到等值面在这一点的法向量
        //Then find the normal to the surface at those points
        for(iEdge = 0; iEdge < 12; iEdge++)
        {
                //if there is an intersection on this edge 如果在这一个边上有交点的话
                if(iEdgeFlags & (1<<iEdge))
                {
                        fOffset = fGetOffset(afCubeValue[ a2iEdgeConnection[iEdge][0] ], 
                                                     afCubeValue[ a2iEdgeConnection[iEdge][1] ], fTargetValue);


                        //计算交点的坐标
                        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;
                       //计算交点的法向量
                        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   画出等值面三角形 每个立方体 5个三角形
        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);
                }
        }
}

//vMarchingCubes iterates over the entire dataset, calling vMarchCube on each cube
GLvoid vMarchingCubes()
{
        GLint iX, iY, iZ;

        glBegin(GL_TRIANGLES);
        for(iX = 0; iX < NX-1; iX++)
        for(iY = 0; iY < NY-1; iY++)
        for(iZ = 0; iZ < NZ-1; iZ++)
        {
                vMarchCube(iX, iY, iZ, 1);
        }
        glEnd();

        printf("finish one Draw ! !n");
}

// 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}
};

4 结果示例

Marching Cube(C++ OpenGl代码)读取医学三维图像*.raw进行三维重建-StubbornHuang Blog

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