球体细分逼近程序：四面体递归细分(C++实现)

本文用C++通过四面体递归细分逼近球体表面，介绍多边形网格细分与计算机图形学中的几何逼近方法。

球体的细分逼近程序

通过递归细分四面体生成球体，三种显示模式：线性框、均匀着色，插值着色

代码

/* 该程序在init()函数中还定义了材质和光源 */
/* mode 0 = 线性框, mode 1 = 均与着色,
mode 3 = 插值着色 */
#include <stdlib.h>
#include<math.h>
#include <GL/glut.h>
typedef float point[4];
/* 初始化四面体 */
point v[]={{0.0, 0.0, 1.0}, {0.0, 0.942809, -0.33333},
    {-0.816497, -0.471405, -0.333333}, {0.816497, -0.471405, -0.333333}};

GLfloat theta[] = {0.0,0.0,0.0};

int n;
int mode;
void triangle( point a, point b, point c)
/*利用GL_LINR_LOOP模式显示一个三角形的线性图，定义一个法向量用于均匀着色，
定义三个法向量用于插值着色*/
{
 if (mode==0)  glBegin(GL_LINE_LOOP);
 else  glBegin(GL_POLYGON);
    if(mode==1) glNormal3fv(a);
    if(mode==2) glNormal3fv(a);
     glVertex3fv(a);
    if(mode==2) glNormal3fv(b);
    glVertex3fv(b);
    if(mode==2) glNormal3fv(c);
    glVertex3fv(c);
 glEnd();
}
void normal(point p)
{
/* 矢量归一化 */
double sqrt(double d);
float d = 0.0;
int i;
for (i = 0; i < 3; i++) d += p[i] * p[i];
d = sqrt(d);
if (d > 0.0)
    for (i = 0; i < 3; i++) p[i] /= d;
}
void divide_triangle(point a, point b, point c, int m)
{
/* 基于顶点数目细分三角形，应用右手规则生成对象的外向表面 */
 point v1, v2, v3;
 int j;
 if(m>0)
 {
    for(j=0; j<3; j++) v1[j]=a[j]+b[j];
    normal(v1);
    for(j=0; j<3; j++) v2[j]=a[j]+c[j];
    normal(v2);
    for(j=0; j<3; j++) v3[j]=b[j]+c[j];
    normal(v3);
    divide_triangle(a, v1, v2, m-1);
    divide_triangle(c, v2, v3, m-1);
    divide_triangle(b, v3, v1, m-1);
    divide_triangle(v1, v3, v2, m-1);
 }
 else triangle(a,b,c); /* 递归结束时绘制三角形 */
}

void tetrahedron(int m)
{
/* 对四面体的表面应用三角细分 */
 divide_triangle(v[0], v[1], v[2], m);
 divide_triangle(v[3], v[2], v[1], m);
 divide_triangle(v[0], v[3], v[1], m);
 divide_triangle(v[0], v[2], v[3], m);
}
void display()
{
/* 逐一显示这三种模式下的四面体 */
 glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
 glLoadIdentity();
 mode=0;
 tetrahedron(n);
 mode=1;
 glTranslatef(-2.0, 0.0, 0.0);
 tetrahedron(n);
 mode=2;
 glTranslatef(4.0, 0.0, 0.0);
 tetrahedron(n);
 glFlush();
}

void myReshape(int w, int h)
{
 glViewport(0, 0, w, h);
 glMatrixMode(GL_PROJECTION);
 glLoadIdentity();
 if (w <= h)
    glOrtho(-4.0, 4.0, -4.0 * (GLfloat) h / (GLfloat) w,
        4.0 * (GLfloat) h / (GLfloat) w, -10.0, 10.0);
 else
    glOrtho(-4.0 * (GLfloat) w / (GLfloat) h,
        4.0 * (GLfloat) w / (GLfloat) h, -4.0, 4.0, -10.0, 10.0);
 glMatrixMode(GL_MODELVIEW);
 display();
}
void myinit()
{
    GLfloat mat_specular[]={1.0, 1.0, 1.0, 1.0};
    GLfloat mat_diffuse[]={1.0, 1.0, 1.0, 1.0};
    GLfloat mat_ambient[]={1.0, 1.0, 1.0, 1.0};
    GLfloat mat_shininess={100.0};
    GLfloat light_ambient[]={0.0, 0.0, 0.0, 1.0};
    GLfloat light_diffuse[]={1.0, 1.0, 1.0, 1.0};
    GLfloat light_specular[]={1.0, 1.0, 1.0, 1.0};
/* 为光源0分别设置环境光、漫反射光和镜面反射光的参数 */
    glLightfv(GL_LIGHT0, GL_AMBIENT, light_ambient);
    glLightfv(GL_LIGHT0, GL_DIFFUSE, light_diffuse);
    glLightfv(GL_LIGHT0, GL_SPECULAR, light_specular);
/* 为所有三角形正面定义材质属性 */
    glMaterialfv(GL_FRONT, GL_SPECULAR, mat_specular);
    glMaterialfv(GL_FRONT, GL_AMBIENT, mat_ambient);
    glMaterialfv(GL_FRONT, GL_DIFFUSE, mat_diffuse);
    glMaterialf(GL_FRONT, GL_SHININESS, mat_shininess);
    glShadeModel(GL_SMOOTH); /* 开启平滑着色 */
    glEnable(GL_LIGHTING); /* 开启光照 */
    glEnable(GL_LIGHT0); /* 开启光源0 */
    glEnable(GL_DEPTH_TEST); /* 开启z-buffer */
    glClearColor (1.0, 1.0, 1.0, 1.0);
    glColor3f (0.0, 0.0, 0.0);
}
main(int argc, char **argv)
{
    n=4;//n=1,2,3,4,5,6……
  //n=atoi(argv[1]);//直接运行会出错，具体参照BookCode的此处源码处理方案
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(500, 500);
    glutCreateWindow("sphere");
    myinit();
    glutReshapeFunc(myReshape);
    glutDisplayFunc(display);
    glutMainLoop();
}

结果