面绘制经典算法：MarchingCube实现(控制台篇)

1.MarchingCube

marchingcube是一个比较经典而古老的算法，也是面绘制中应用比较多的算法，Marchingcube发展到今天也遇到了几何拓扑、一致性的问题仍待改善。本文研究的就是经典的marchingcube(Paul,1997).

关于MarchingCube原理（含代码），重点推荐如下：

1.《医学图像三维重建和可视化:VC++实现实例》(张俊华)

2.Bourke P. Polygonising a scalar field[J]. 1997.

3.论文+源代码+交互界面

2.控制台上实现与讨论

算法设计步骤：

1.二维断层图像顺序地读入内存并构成三位数据场；

2.依次扫描相邻两层数据，逐个构造立方体；

3.将立方体每个顶点灰度和给定等值面阈值进行比较，计算索引值；

4.对于含有等值面的立方体，通过灰度差分计算立方体各顶点的梯度；

5.根据索引值查找边索引表，获得和等值面有交点的当前立方体的相交边；

6.根据相交边的两个顶点坐标及其法向量，利用差值（中值）计算等值点的坐标与法向量；

7.根据索引值查找三角片索引表，确定当前立方体内构成三角片的等值点的组合方式；

8.由各个立方体内的三角面片构成等值面。

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <iostream>
using namespace std;

static int edgeTable[256]={ }; //根据索引值确定立方体和等值面交点情况
static int triTable[256][16] ={ };//根据索引值确定三角面片的个数以及位置

typedef struct
{
double x,y,z;
} XYZ;

typedef struct
{
XYZ p[8]; //顶点坐标
XYZ n[8]; //法向量
double val[8]; //顶点对应的灰度值
} GRIDCELL; //立方体

typedef struct
{
XYZ p[3]; //顶点坐标
XYZ c; //几何中心
XYZ n[3]; //法向量
} TRIANGLE;

#define ABS(x) (x < 0 ? -(x) : (x))

//声明
int PolygoniseCube(GRIDCELL , double , TRIANGLE * );
XYZ VertexInterp(double , XYZ , XYZ , double, double );

//3D数据场大小
#define NX 200
#define NY 160
#define NZ 160

int main( int argc, char **argv)
{
short int*** data = NULL;
short int isolevel = 128, themax = 0, themin = 255; //等值面 数据场的范围
GRIDCELL grid;
TRIANGLE triangles[10];
TRIANGLE* tri = NULL; //保存的是所有三角形面片的顶点坐标

int ntri = 0;
FILE* fptr = NULL;

//打开并阅读原始文件
fprintf(stderr, "Reading data...\n");
errno_t err;
err = fopen_s(&fptr,"mri.raw", "rb");
if( err != NULL ) {
fprintf(stderr, "File open failed\n");
exit(-1);
}

//为三维数据场分配空间
data = (short int***) malloc( NX * sizeof(short int **) );
for (int i=0;i<NX;i++)
data[i] = (short int**) malloc( NY * sizeof(short int *));
for (int i=0;i<NX;i++)
for (int j=0;j<NY;j++)
data[i][j] = (short int*) malloc(NZ * sizeof(short int));

int str; //从文件中读取字符
for (int k=0; k<NZ; k++){
for(int j=0; j<NY; j++){
for(int i=0; i<NX; i++){
if ((str = fgetc(fptr)) == EOF) { //fgetc顺序读取数据，直到遇见-文件结束符EOF
fprintf(stderr,"Unexpected end of file\n");
exit(-1);
}
data[i][j][k] = str;
if( str > themax )
themax = str;
if( str < themin )
themin = str;
}
}
}
fclose(fptr);
fprintf(stderr,"Volumetric data range: %d -> %d\n",themin,themax);

//3D数据场处理
fprintf(stderr, "polygonising data...\n");
for (int i=0; i<NX-1; i++)
{
if(i % (NX/10) == 0)
fprintf(stderr, " Slice %d of %d \n", i, NX);

for (int j=0; j<NY-1; j++){
for (int k=0; k<NZ-1; k++){
grid.p[0].x = i; grid.p[0].y = j; grid.p[0].z = k; grid.val[0] = data[i] [j] [k];
grid.p[1].x = i+1;grid.p[1].y = j; grid.p[1].z = k; grid.val[1] = data[i+1][j] [k];
grid.p[2].x = i+1;grid.p[2].y = j+1;grid.p[2].z = k; grid.val[2] = data[i+1][j+1][k];
grid.p[3].x = i; grid.p[3].y = j+1;grid.p[3].z = k; grid.val[3] = data[i] [j+1][k];

grid.p[4].x = i; grid.p[4].y = j; grid.p[4].z = k+1;grid.val[4] = data[i] [j] [k+1];
grid.p[5].x = i+1;grid.p[5].y = j; grid.p[5].z = k+1;grid.val[5] = data[i+1][j] [k+1];
grid.p[6].x = i+1;grid.p[6].y = j+1;grid.p[6].z = k+1;grid.val[6] = data[i+1][j+1][k+1];
grid.p[7].x = i; grid.p[7].y = j+1;grid.p[7].z = k+1;grid.val[7] = data[i] [j+1][k+1];
//计算当前立方体中的三角面片数目
int numOftriangle = PolygoniseCube(grid, isolevel, triangles);
tri = (TRIANGLE*) realloc(tri , (ntri + numOftriangle) * sizeof(TRIANGLE) );
for (int i=0; i<numOftriangle; i++) //将当前立方体中包含的三角面片保存
tri[ntri+i] = triangles[i];
ntri += numOftriangle;
}
}
}
fprintf(stderr,"Total of %d triangles\n",ntri);

// Now do something with the triangles .... Here I just write them to a geom file
fprintf(stderr,"Writing triangles ...\n");
if ((fopen_s (&fptr,"output.geom","w")) != NULL) {
fprintf(stderr,"Failed to open output file\n");
exit(-1);
}

for (int i=0;i<ntri;i++) {
fprintf(fptr,"f3 ");
for (int k=0;k<3;k++) {
fprintf(fptr,"%g %g %g ",tri[i].p[k].x,tri[i].p[k].y,tri[i].p[k].z);
}
fprintf(fptr,"0.5 0.5 0.5\n"); // colour
}
fclose(fptr);
free(data); //释放堆上的内存
exit(0);
}
/*/////////////////////////////////////////////////////////////////////////

4--------5 *---4----*
/| /| /| /|
/ | / | 7 | 5 |
/ | / | / 8 / 9
7--------6 | *----6---* |
| | | | | | | |
| 0----|---1 | *---0|---*
| / | / 11 / 10 /
| / | / | 3 | 1
|/ |/ |/ |/
3--------2 *---2----*
////////////////////////////////////////////////////////////////////////////*/
int PolygoniseCube(GRIDCELL grid, double isolevel, TRIANGLE* tri)
{
int numOftriangle = 0;
int cubeIndex = 0;
XYZ vertlist[12]; //保存等值面与立方体各边相交的坐标
//确定那个顶点位于等值面内部
if (grid.val[0] < isolevel) cubeIndex |= 1;
if (grid.val[1] < isolevel) cubeIndex |= 2;
if (grid.val[2] < isolevel) cubeIndex |= 4;
if (grid.val[3] < isolevel) cubeIndex |= 8;
if (grid.val[4] < isolevel) cubeIndex |= 16;
if (grid.val[5] < isolevel) cubeIndex |= 32;
if (grid.val[6] < isolevel) cubeIndex |= 64;
if (grid.val[7] < isolevel) cubeIndex |= 128;

//异常：立方体所有顶点都在或者都不在等值面内部
if ( edgeTable[cubeIndex] == 0 )
return 0;
//确定等值面与立方体交点坐标
if (edgeTable[cubeIndex] & 1) {
vertlist[0] = VertexInterp(isolevel,grid.p[0],grid.p[1],grid.val[0],grid.val[1]);
}
if (edgeTable[cubeIndex] & 2) {
vertlist[1] = VertexInterp(isolevel,grid.p[1],grid.p[2],grid.val[1],grid.val[2]);
}
if (edgeTable[cubeIndex] & 4) {
vertlist[2] = VertexInterp(isolevel,grid.p[2],grid.p[3],grid.val[2],grid.val[3]);
}
if (edgeTable[cubeIndex] & 8) {
vertlist[3] = VertexInterp(isolevel,grid.p[3],grid.p[0],grid.val[3],grid.val[0]);
}
if (edgeTable[cubeIndex] & 16) {
vertlist[4] = VertexInterp(isolevel,grid.p[4],grid.p[5],grid.val[4],grid.val[5]);
}
if (edgeTable[cubeIndex] & 32) {
vertlist[5] = VertexInterp(isolevel,grid.p[5],grid.p[6],grid.val[5],grid.val[6]);
}
if (edgeTable[cubeIndex] & 64) {
vertlist[6] = VertexInterp(isolevel,grid.p[6],grid.p[7],grid.val[6],grid.val[7]);
}
if (edgeTable[cubeIndex] & 128) {
vertlist[7] = VertexInterp(isolevel,grid.p[7],grid.p[4],grid.val[7],grid.val[4]);
}
if (edgeTable[cubeIndex] & 256) {
vertlist[8] = VertexInterp(isolevel,grid.p[0],grid.p[4],grid.val[0],grid.val[4]);
}
if (edgeTable[cubeIndex] & 512) {
vertlist[9] = VertexInterp(isolevel,grid.p[1],grid.p[5],grid.val[1],grid.val[5]);
}
if (edgeTable[cubeIndex] & 1024) {
vertlist[10] = VertexInterp(isolevel,grid.p[2],grid.p[6],grid.val[2],grid.val[6]);
}
if (edgeTable[cubeIndex] & 2048) {
vertlist[11] = VertexInterp(isolevel,grid.p[3],grid.p[7],grid.val[3],grid.val[7]);
}
//根据交点坐标确定三角形面片，并进行保存
for (int i=0; triTable[cubeIndex][i] != -1; i+=3)
{
tri[numOftriangle].p[0] = vertlist[ triTable[cubeIndex][i ] ];
tri[numOftriangle].p[1] = vertlist[ triTable[cubeIndex][i+1] ];
tri[numOftriangle].p[2] = vertlist[ triTable[cubeIndex][i+2] ];
numOftriangle++;
}

return (numOftriangle);
}
//等值面与立方体交点坐标
XYZ VertexInterp(double isolevel, XYZ p1, XYZ p2, double valp1, double valp2)
{
XYZ p;
if (ABS(isolevel-valp1) < 0.00001)
return(p1);
if (ABS(isolevel-valp2) < 0.00001)
return(p2);
if (ABS(valp1-valp2) < 0.00001)
return(p1);

double coef = (isolevel - valp1 ) / (valp2 - valp1);
p.x = p1.x + coef * (p2.x - p1.x);
p.y = p1.y + coef * (p2.y - p1.y);
p.z = p1.z + coef * (p2.z - p1.z);

return (p);
}

3.学习心得

1.学会定义结构体，例如三维空间的立方体，需要先定义一个坐标XYZ结构体，然后再定义一个立方体结构体，而他们之间恰恰是相互依赖的。

typedef struct
{
double x,y,z;
} XYZ;

typedef struct
{
XYZ p[8]; //顶点坐标
XYZ n[8]; //法向量
double val[8]; //顶点对应的灰度值
} GRIDCELL; //立方体2.如何动态为三位数据场分配空间？
data = (short int***) malloc( NX * sizeof(short int **) );
for (int i=0;i<NX;i++)
data[i] = (short int**) malloc( NY * sizeof(short int *));
for (int i=0;i<NX;i++)
for (int j=0;j<NY;j++)
data[i][j] = (short int*) malloc(NZ * sizeof(short int));我们要注意到，利用malloc()函数进行内存申请之后返回来的是void*型的指针，我们需要进行指针的强制类型转换。该段代码也给我一个很深的感悟就是"指针确实是一门艺术"。
3.读取文件以及数据元素读取

errno_t err;
err = fopen_s(&fptr,"mri.raw", "rb");
if( err != NULL ) {
fprintf(stderr, "File open failed\n");
exit(-1);
}读取文件可以采用fopen或fopen_s两个函数，不同之处在于前者需要提供两个参数，并返回FILE*类型；而后者需要提供三个参数，返回的是errno_t(实质就是int的别名)类型。相比较而言，fopen_s更安全。

int str; //从文件中读取字符
for (int k=0; k<NZ; k++){
for(int j=0; j<NY; j++){
for(int i=0; i<NX; i++){
if ((str = fgetc(fptr)) == EOF) {
fprintf(stderr,"Unexpected end of file\n");
exit(-1);
}
data[i][j][k] = str;

}
}
}

fgetc()顺序读取数据。