opengl实现bezier曲面,要求用不同颜色显 示曲面和曲面的控制网格,并且可以取消曲面控制网格的显示,允 许交互式地改变控制网格的定点位置,以观看曲面形状的改变;能 够通过对话框、菜单等方式设置曲面的配置参数（书写代码）

下面是OpenGL实现Bezier曲面的代码，包含了不同颜色显示曲面和控制网格、交互式改变控制点、设置曲面参数等功能。具体实现过程请参考注释。

#include <GL/glut.h>

const int WIDTH = 800;  // 窗口宽度
const int HEIGHT = 600; // 窗口高度

const int MAX_GRID = 20; // 控制网格最大点数
const int MAX_T = 100;   // 参数t的最大值

bool show_grid = true;   // 是否显示控制网格

int grid_size = 4;       // 控制网格大小
int curve_size = 2;      // 曲面线宽
int point_size = 5;      // 控制点大小

int grid[MAX_GRID][MAX_GRID][3]; // 控制网格点坐标
int grid_num_u;         // 控制网格u方向点数
int grid_num_v;         // 控制网格v方向点数

float bezier[MAX_T][MAX_T][3];   // Bezier曲面上的点坐标
float t_step = 0.01;    // 参数t的步长

// 初始化控制网格
void init_grid() {
    grid_num_u = 4;
    grid_num_v = 4;
    for (int i = 0; i < grid_num_u; ++i) {
        for (int j = 0; j < grid_num_v; ++j) {
            grid[i][j][0] = i * 100 / (grid_num_u - 1);
            grid[i][j][1] = j * 100 / (grid_num_v - 1);
            grid[i][j][2] = 0;
        }
    }
}

// 计算Bezier曲面上的点坐标
void calculate_bezier() {
    for (int i = 0; i < MAX_T; ++i) {
        float t_u = i * t_step;
        for (int j = 0; j < MAX_T; ++j) {
            float t_v = j * t_step;
            float x = 0.0, y = 0.0, z = 0.0;
            for (int k = 0; k < grid_num_u; ++k) {
                for (int l = 0; l < grid_num_v; ++l) {
                    float b_u = 1.0, b_v = 1.0;
                    for (int m = 0; m < grid_num_u; ++m) {
                        if (m == k) continue;
                        b_u *= (t_u - m * t_step) / (k * t_step - m * t_step);
                    }
                    for (int m = 0; m < grid_num_v; ++m) {
                        if (m == l) continue;
                        b_v *= (t_v - m * t_step) / (l * t_step - m * t_step);
                    }
                    x += grid[k][l][0] * b_u * b_v;
                    y += grid[k][l][1] * b_u * b_v;
                    z += grid[k][l][2] * b_u * b_v;
                }
            }
            bezier[i][j][0] = x;
            bezier[i][j][1] = y;
            bezier[i][j][2] = z;
        }
    }
}

// 绘制Bezier曲面
void draw_bezier() {
    glLineWidth(curve_size);
    glColor3f(1.0, 0.0, 0.0);
    for (int i = 0; i < MAX_T - 1; ++i) {
        for (int j = 0; j < MAX_T - 1; ++j) {
            glBegin(GL_LINE_LOOP);
            glVertex3fv(bezier[i][j]);
            glVertex3fv(bezier[i+1][j]);
            glVertex3fv(bezier[i+1][j+1]);
            glVertex3fv(bezier[i][j+1]);
            glEnd();
        }
    }
}

// 绘制控制网格
void draw_grid() {
    glPointSize(point_size);
    glBegin(GL_POINTS);
    glColor3f(0.0, 1.0, 0.0);
    for (int i = 0; i < grid_num_u; ++i) {
        for (int j = 0; j < grid_num_v; ++j) {
            glVertex3iv(grid[i][j]);
        }
    }
    glEnd();

    glLineWidth(curve_size);
    glBegin(GL_LINES);
    glColor3f(0.0, 0.0, 1.0);
    for (int i = 0; i < grid_num_u; ++i) {
        for (int j = 0; j < grid_num_v - 1; ++j) {
            glVertex3iv(grid[i][j]);
            glVertex3iv(grid[i][j+1]);
        }
    }
    for (int i = 0; i < grid_num_u - 1; ++i) {
        for (int j = 0; j < grid_num_v; ++j) {
            glVertex3iv(grid[i][j]);
            glVertex3iv(grid[i+1][j]);
        }
    }
    glEnd();
}

// 鼠标事件回调函数
void mouse(int button, int state, int x, int y) {
    if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN) {
        // 将鼠标坐标从窗口坐标系转换到OpenGL坐标系
        float ox = (float)x / WIDTH * 2 - 1;
        float oy = 1 - (float)y / HEIGHT * 2;

        // 在控制网格中查找最近的点
        int min_dist = INT_MAX;
        int u = -1, v = -1;
        for (int i = 0; i < grid_num_u; ++i) {
            for (int j = 0; j < grid_num_v; ++j) {
                int dx = ox * 100 - grid[i][j][0];
                int dy = oy * 100 - grid[i][j][1];
                int dist = dx * dx + dy * dy;
                if (dist < min_dist) {
                    min_dist = dist;
                    u = i;
                    v = j;
                }
            }
        }

        // 更新控制点位置
        grid[u][v][0] = ox * 100;
        grid[u][v][1] = oy * 100;

        // 重新计算Bezier曲面上的点
        calculate_bezier();

        // 重绘窗口
        glutPostRedisplay();
    }
}

// 菜单事件回调函数
void menu(int value) {
    switch (value) {
        case 1:
            show_grid = !show_grid;
            break;
        case 2:
            grid_size++;
            if (grid_size > 10) grid_size = 10;
            break;
        case 3:
            grid_size--;
            if (grid_size < 1) grid_size = 1;
            break;
        case 4:
            curve_size++;
            if (curve_size > 10) curve_size = 10;
            break;
        case 5:
            curve_size--;
            if (curve_size < 1) curve_size = 1;
            break;
        case 6:
            point_size++;
            if (point_size > 10) point_size = 10;
            break;
        case 7:
            point_size--;
            if (point_size < 1) point_size = 1;
            break;
        case 8:
            t_step += 0.001;
            if (t_step > 0.1) t_step = 0.1;
            calculate_bezier();
            break;
        case 9:
            t_step -= 0.001;
            if (t_step < 0.001) t_step = 0.001;
            calculate_bezier();
            break;
        case 10:
            init_grid();
            calculate_bezier();
            break;
    }

    // 重绘窗口
    glutPostRedisplay();
}

// 初始化OpenGL
void init() {
    glClearColor(1.0, 1.0, 1.0, 1.0);
    glEnable(GL_DEPTH_TEST);

    init_grid();
    calculate_bezier();

    // 创建菜单
    glutCreateMenu(menu);
    glutAddMenuEntry("Toggle Grid", 1);
    glutAddMenuEntry("Enlarge Grid", 2);
    glutAddMenuEntry("Shrink Grid", 3);
    glutAddMenuEntry("Enlarge Curve", 4);
    glutAddMenuEntry("Shrink Curve", 5);
    glutAddMenuEntry("Enlarge Points", 6);
    glutAddMenuEntry("Shrink Points", 7);
    glutAddMenuEntry("Increase t_step", 8);
    glutAddMenuEntry("Decrease t_step", 9);
    glutAddMenuEntry("Reset", 10);
    glutAttachMenu(GLUT_RIGHT_BUTTON);
}

// 窗口大小变化事件回调函数
void reshape(int width, int height) {
    glViewport(0, 0, width, height);
    glMatrixMode(GL_PROJECTION);
    glLoadIdentity();
    gluPerspective(60.0, (double)width / height, 0.1, 1000.0);
    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluLookAt(0.0, 0.0, 200.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0);
}

// 渲染函数
void display() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glPushMatrix();

    // 绘制Bezier曲面
    draw_bezier();

    // 绘制控制网格
    if (show_grid) {
        draw_grid();
    }

    glPopMatrix();

    glutSwapBuffers();
}

int main(int argc, char** argv) {
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(WIDTH, HEIGHT);
    glutCreateWindow("Bezier Surface");

    glutMouseFunc(mouse);
    glutReshapeFunc(reshape);
    glutDisplayFunc(display);

    init();

    glutMainLoop();

    return 0;
}