计算机图形学正十二面体代码

以下是使用OpenGL库绘制正十二面体的代码示例：

#include <iostream>
#include <cmath>
#include <GL/glut.h>

// 定义正十二面体的顶点坐标
GLfloat vertices[20][3] = {
    {-1.0f, 0.0f, 1.0f},
    {1.0f, 0.0f, 1.0f},
    {1.0f, 0.0f, -1.0f},
    {-1.0f, 0.0f, -1.0f},
    {0.0f, 1.0f, 0.0f},
    {0.0f, -1.0f, 0.0f},
    {0.0f, 0.0f, 2.0f},
    {0.0f, 0.0f, -2.0f},
    {1.0f, 1.0f, 1.0f},
    {-1.0f, 1.0f, 1.0f},
    {-1.0f, -1.0f, 1.0f},
    {1.0f, -1.0f, 1.0f},
    {-1.0f, 1.0f, -1.0f},
    {1.0f, 1.0f, -1.0f},
    {1.0f, -1.0f, -1.0f},
    {-1.0f, -1.0f, -1.0f},
    {1.0f, 1.0f, 0.0f},
    {0.0f, 1.0f, 1.0f},
    {-1.0f, 1.0f, 0.0f},
    {0.0f, 1.0f, -1.0f}
};

// 定义正十二面体的面索引
int faces[32][3] = {
    {0, 8, 1},
    {1, 9, 2},
    {2, 10, 3},
    {3, 11, 0},
    {8, 4, 9},
    {9, 5, 10},
    {10, 6, 11},
    {11, 7, 8},
    {4, 0, 5},
    {5, 1, 6},
    {6, 2, 7},
    {7, 3, 4},
    {5, 0, 8},
    {6, 1, 9},
    {7, 2, 10},
    {4, 3, 11},
    {12, 13, 14},
    {12, 14, 15},
    {12, 15, 16},
    {12, 16, 13},
    {13, 17, 14},
    {14, 18, 15},
    {15, 19, 16},
    {16, 17, 13},
    {17, 18, 14},
    {18, 19, 15},
    {19, 17, 16},
    {17, 19, 18},
};

// 绘制正十二面体
void drawDodecahedron() {
    glBegin(GL_TRIANGLES);
    for (int i = 0; i < 32; i++) {
        int a = faces[i][0];
        int b = faces[i][1];
        int c = faces[i][2];
        GLfloat v1[3] = {vertices[a][0], vertices[a][1], vertices[a][2]};
        GLfloat v2[3] = {vertices[b][0], vertices[b][1], vertices[b][2]};
        GLfloat v3[3] = {vertices[c][0], vertices[c][1], vertices[c][2]};
        // 计算面法线
        GLfloat normal[3];
        normal[0] = (v1[1] - v2[1]) * (v3[2] - v2[2]) - (v1[2] - v2[2]) * (v3[1] - v2[1]);
        normal[1] = (v1[2] - v2[2]) * (v3[0] - v2[0]) - (v1[0] - v2[0]) * (v3[2] - v2[2]);
        normal[2] = (v1[0] - v2[0]) * (v3[1] - v2[1]) - (v1[1] - v2[1]) * (v3[0] - v2[0]);
        glNormal3fv(normal);
        glVertex3fv(v1);
        glVertex3fv(v2);
        glVertex3fv(v3);
    }
    glEnd();
}

// 初始化OpenGL环境
void init() {
    glClearColor(0.0f, 0.0f, 0.0f, 0.0f);
    glEnable(GL_DEPTH_TEST);
    glEnable(GL_LIGHTING);
    glEnable(GL_LIGHT0);
    GLfloat light_position[] = {1.0f, 1.0f, 1.0f, 0.0f};
    glLightfv(GL_LIGHT0, GL_POSITION, light_position);
}

// 渲染回调函数
void display() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluLookAt(0.0f, 0.0f, 5.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f);
    glRotatef(30.0f, 1.0f, 1.0f, 1.0f);
    glColor3f(1.0f, 0.0f, 0.0f);
    drawDodecahedron();
    glutSwapBuffers();
}

// 窗口大小变化回调函数
void reshape(int w, int h) {
    glViewport(0, 0, w, h);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(45.0f, (float)w / (float)h, 0.1f, 100.0f);
}

int main(int argc, char **argv) {
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(800, 600);
    glutCreateWindow("Dodecahedron");
    init();
    glutDisplayFunc(display);
    glutReshapeFunc(reshape);
    glutMainLoop();
    return 0;
}

这里使用了OpenGL库来进行图形绘制和渲染。如果您需要使用其他图形库或语言来绘制正十二面体，可以根据需要进行修改。