在vs中用c++绘制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；（书写具体代码）

以下是一个基本的实现代码，实现了Bezier曲面的绘制、控制网格的显示和交互式修改控制点位置。同时，也可以通过菜单设置曲面的配置参数。

#include <windows.h>
#include <GL/gl.h>
#include <GL/glu.h>
#include <iostream>
#include <vector>

using namespace std;

// 控制点信息
struct Point {
    GLfloat x, y, z;
};

// 配置参数
struct Config {
    int u_num;  // u方向控制点数目
    int v_num;  // v方向控制点数目
    GLfloat step_u;  // u方向步长
    GLfloat step_v;  // v方向步长
    bool show_grid;  // 是否显示控制网格
};

// 全局变量
vector<Point> control_points;  // 控制点数组
Config config = {4, 4, 0.1f, 0.1f, true};  // 默认配置参数
GLfloat rotate_x = 0.0f;  // x轴旋转角度
GLfloat rotate_y = 0.0f;  // y轴旋转角度
bool dragging = false;  // 是否正在拖拽控制点
int dragging_index = -1;  // 正在拖拽的控制点的下标

// 绘制控制点
void drawControlPoints() {
    glColor3f(1.0f, 0.0f, 0.0f);
    glPointSize(5.0f);
    glBegin(GL_POINTS);
    for (int i = 0; i < control_points.size(); ++i) {
        glVertex3f(control_points[i].x, control_points[i].y, control_points[i].z);
    }
    glEnd();
}

// 绘制控制网格
void drawControlGrid() {
    glColor3f(0.5f, 0.5f, 0.5f);
    glBegin(GL_LINES);
    for (int i = 0; i < config.u_num; ++i) {
        for (int j = 0; j < config.v_num; ++j) {
            if (i < config.u_num - 1) {
                glVertex3f(control_points[i * config.v_num + j].x, control_points[i * config.v_num + j].y, control_points[i * config.v_num + j].z);
                glVertex3f(control_points[(i + 1) * config.v_num + j].x, control_points[(i + 1) * config.v_num + j].y, control_points[(i + 1) * config.v_num + j].z);
            }
            if (j < config.v_num - 1) {
                glVertex3f(control_points[i * config.v_num + j].x, control_points[i * config.v_num + j].y, control_points[i * config.v_num + j].z);
                glVertex3f(control_points[i * config.v_num + j + 1].x, control_points[i * config.v_num + j + 1].y, control_points[i * config.v_num + j + 1].z);
            }
        }
    }
    glEnd();
}

// 绘制Bezier曲面
void drawBezierSurface() {
    glColor3f(0.0f, 1.0f, 0.0f);
    for (int i = 0; i < config.u_num - 3; ++i) {
        for (int j = 0; j < config.v_num - 3; ++j) {
            glBegin(GL_QUADS);
            for (GLfloat u = 0.0f; u <= 1.0f; u += config.step_u) {
                for (GLfloat v = 0.0f; v <= 1.0f; v += config.step_v) {
                    GLfloat p[3];
                    GLfloat q[4];
                    GLfloat r[4];
                    for (int k = 0; k < 4; ++k) {
                        q[k] = control_points[(i + k) * config.v_num + j].x * (1 - v) + control_points[(i + k) * config.v_num + j + 1].x * v;
                        r[k] = control_points[(i + k) * config.v_num + j].y * (1 - v) + control_points[(i + k) * config.v_num + j + 1].y * v;
                    }
                    p[0] = q[0] * (1 - u) * (1 - u) * (1 - u) + 3 * q[1] * u * (1 - u) * (1 - u) + 3 * q[2] * u * u * (1 - u) + q[3] * u * u * u;
                    p[1] = r[0] * (1 - u) * (1 - u) * (1 - u) + 3 * r[1] * u * (1 - u) * (1 - u) + 3 * r[2] * u * u * (1 - u) + r[3] * u * u * u;
                    p[2] = control_points[(i + 1) * config.v_num + j + 1].z * v + control_points[(i + 1) * config.v_num + j].z * (1 - v);
                    glVertex3f(p[0], p[1], p[2]);
                }
            }
            glEnd();
        }
    }
}

// 绘制函数
void display() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT);

    glMatrixMode(GL_MODELVIEW);
    glLoadIdentity();
    gluLookAt(0.0f, 0.0f, 10.0f, 0.0f, 0.0f, 0.0f, 0.0f, 1.0f, 0.0f);
    glRotatef(rotate_x, 1.0f, 0.0f, 0.0f);
    glRotatef(rotate_y, 0.0f, 1.0f, 0.0f);

    if (config.show_grid) {
        drawControlGrid();
    }
    drawBezierSurface();
    drawControlPoints();

    glFlush();
}

// 初始化函数
void init() {
    glClearColor(1.0f, 1.0f, 1.0f, 1.0f);
    glEnable(GL_DEPTH_TEST);
}

// 鼠标按下事件
void mouseClick(int button, int state, int x, int y) {
    if (button == GLUT_LEFT_BUTTON && state == GLUT_DOWN) {
        GLint viewport[4];
        GLdouble modelview[16];
        GLdouble projection[16];
        GLfloat winX, winY, winZ;
        GLdouble posX, posY, posZ;

        glGetDoublev(GL_MODELVIEW_MATRIX, modelview);
        glGetDoublev(GL_PROJECTION_MATRIX, projection);
        glGetIntegerv(GL_VIEWPORT, viewport);

        winX = (float)x;
        winY = (float)viewport[3] - (float)y;
        glReadPixels(x, int(winY), 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ);

        gluUnProject(winX, winY, winZ, modelview, projection, viewport, &posX, &posY, &posZ);

        for (int i = 0; i < control_points.size(); ++i) {
            GLfloat dist = sqrt(pow(posX - control_points[i].x, 2) + pow(posY - control_points[i].y, 2) + pow(posZ - control_points[i].z, 2));
            if (dist < 0.2f) {
                dragging = true;
                dragging_index = i;
                break;
            }
        }
    } else if (button == GLUT_LEFT_BUTTON && state == GLUT_UP) {
        dragging = false;
        dragging_index = -1;
    }
}

// 鼠标拖拽事件
void mouseDrag(int x, int y) {
    if (dragging) {
        GLint viewport[4];
        GLdouble modelview[16];
        GLdouble projection[16];
        GLfloat winX, winY, winZ;
        GLdouble posX, posY, posZ;

        glGetDoublev(GL_MODELVIEW_MATRIX, modelview);
        glGetDoublev(GL_PROJECTION_MATRIX, projection);
        glGetIntegerv(GL_VIEWPORT, viewport);

        winX = (float)x;
        winY = (float)viewport[3] - (float)y;
        glReadPixels(x, int(winY), 1, 1, GL_DEPTH_COMPONENT, GL_FLOAT, &winZ);

        gluUnProject(winX, winY, winZ, modelview, projection, viewport, &posX, &posY, &posZ);

        control_points[dragging_index].x = posX;
        control_points[dragging_index].y = posY;
        control_points[dragging_index].z = posZ;

        glutPostRedisplay();
    }
}

// 菜单处理函数
void menuHandler(int value) {
    switch (value) {
        case 1:
            config.u_num = 4;
            config.v_num = 4;
            config.step_u = 0.1f;
            config.step_v = 0.1f;
            break;
        case 2:
            config.u_num = 5;
            config.v_num = 5;
            config.step_u = 0.05f;
            config.step_v = 0.05f;
            break;
        case 3:
            config.u_num = 8;
            config.v_num = 8;
            config.step_u = 0.01f;
            config.step_v = 0.01f;
            break;
        case 4:
            config.show_grid = !config.show_grid;
            break;
    }

    glutPostRedisplay();
}

// 创建菜单
void createMenu() {
    int submenu1 = glutCreateMenu(menuHandler);
    glutAddMenuEntry("4x4", 1);
    glutAddMenuEntry("5x5", 2);
    glutAddMenuEntry("8x8", 3);

    int submenu2 = glutCreateMenu(menuHandler);
    glutAddMenuEntry("显示控制网格", 4);

    glutCreateMenu(menuHandler);
    glutAddSubMenu("设置控制点数目", submenu1);
    glutAddSubMenu("显示选项", submenu2);
    glutAttachMenu(GLUT_RIGHT_BUTTON);
}

// 主函数
int main(int argc, char** argv) {
    glutInit(&argc, argv);
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB | GLUT_DEPTH);
    glutInitWindowSize(640, 480);
    glutCreateWindow("Bezier曲面");

    init();

    control_points.push_back({-1.0f, -1.0f, 0.0f});
    control_points.push_back({-0.5f, -1.0f, 1.0f});
    control_points.push_back({0.5f, -1.0f, -1.0f});
    control_points.push_back({1.0f, -1.0f, 0.0f});
    control_points.push_back({-1.0f, 0.0f, 1.0f});
    control_points.push_back({-0.5f, 0.0f, -1.0f});
    control_points.push_back({0.5f, 0.0f, 1.0f});
    control_points.push_back({1.0f, 0.0f, -1.0f});
    control_points.push_back({-1.0f, 1.0f, 0.0f});
    control_points.push_back({-0.5f, 1.0f, -1.0f});
    control_points.push_back({0.5f, 1.0f, 1.0f});
    control_points.push_back({1.0f, 1.0f, 0.0f});

    glutDisplayFunc(display);
    glutMouseFunc(mouseClick);
    glutMotionFunc(mouseDrag);
    createMenu();

    glutMainLoop();

    return 0;
}