在vs中用c++绘制bezier曲面并改变网格定点位置(书写代码)

以下是一个简单的示例代码，可以在 Visual Studio 中使用 C++ 绘制一个 Bezier 曲面，并通过改变网格定点位置来调整曲面形状：

#include <iostream>
#include <vector>
#include <cmath>
#include <GL/glut.h> // OpenGL 窗口库头文件

using namespace std;

const int WINDOW_WIDTH = 800;
const int WINDOW_HEIGHT = 600;
const float PI = 3.1415926f;

// 定义控制点数组，共有 16 个点，用于构建 4x4 网格
vector<float> controlPoints = {
    -1.5f, -1.5f, 4.0f, -0.5f, -1.5f, 2.0f, 0.5f, -1.5f, -1.0f, 1.5f, -1.5f, -2.0f,
    -1.5f, -0.5f, 1.5f, -0.5f, -0.5f, 3.0f, 0.5f, -0.5f, 0.0f, 1.5f, -0.5f, -1.0f,
    -1.5f, 0.5f, 4.0f, -0.5f, 0.5f, 0.0f, 0.5f, 0.5f, 3.0f, 1.5f, 0.5f, 4.0f,
    -1.5f, 1.5f, -2.0f, -0.5f, 1.5f, -0.5f, 0.5f, 1.5f, -1.0f, 1.5f, 1.5f, 2.0f
};

// 定义网格数组，共有 16x3 个点，用于绘制 4x4 网格
vector<float> gridPoints;

// 定义 Bezier 曲面的阶数
const int ORDER = 3;

// 计算组合数
int nChoosek(int n, int k) {
    if (k > n) return 0;
    if (k == 0) return 1;
    return nChoosek(n-1, k-1) * n / k;
}

// 计算 Bezier 基函数
float basisFunc(int i, int k, float t) {
    return nChoosek(ORDER, i) * pow(t, i) * pow(1-t, ORDER-i);
}

// 计算 Bezier 曲面上某个点的坐标
vector<float> computePointOnSurface(float u, float v) {
    vector<float> point = {0, 0, 0};
    for (int i = 0; i <= ORDER; i++) {
        for (int j = 0; j <= ORDER; j++) {
            float basis = basisFunc(i, ORDER, u) * basisFunc(j, ORDER, v);
            int index = (i * (ORDER+1) + j) * 3;
            point[0] += controlPoints[index] * basis;
            point[1] += controlPoints[index+1] * basis;
            point[2] += controlPoints[index+2] * basis;
        }
    }
    return point;
}

// 初始化 OpenGL
void init() {
    // 设置清空颜色为黑色
    glClearColor(0.0f, 0.0f, 0.0f, 1.0f);

    // 计算网格点坐标
    for (float v = 0; v <= 1.0f; v += 0.1f) {
        for (float u = 0; u <= 1.0f; u += 0.1f) {
            vector<float> point = computePointOnSurface(u, v);
            gridPoints.push_back(point[0]);
            gridPoints.push_back(point[1]);
            gridPoints.push_back(point[2]);
        }
    }
}

// 绘制 Bezier 曲面
void drawBezierSurface() {
    // 设置颜色为白色
    glColor3f(1.0f, 1.0f, 1.0f);

    // 绘制曲面
    glBegin(GL_QUADS);
    for (int i = 0; i < 9; i++) {
        for (int j = 0; j < 9; j++) {
            int index1 = (i * 10 + j) * 3;
            int index2 = ((i+1) * 10 + j) * 3;
            int index3 = ((i+1) * 10 + j+1) * 3;
            int index4 = (i * 10 + j+1) * 3;

            glVertex3f(gridPoints[index1], gridPoints[index1+1], gridPoints[index1+2]);
            glVertex3f(gridPoints[index2], gridPoints[index2+1], gridPoints[index2+2]);
            glVertex3f(gridPoints[index3], gridPoints[index3+1], gridPoints[index3+2]);
            glVertex3f(gridPoints[index4], gridPoints[index4+1], gridPoints[index4+2]);
        }
    }
    glEnd();

    // 绘制网格
    glColor3f(0.5f, 0.5f, 0.5f);
    glBegin(GL_LINES);
    for (int i = 0; i < 10; i++) {
        for (int j = 0; j < 10; j++) {
            int index1 = (i * 10 + j) * 3;
            int index2 = (i * 10 + j+1) * 3;
            int index3 = ((i+1) * 10 + j) * 3;
            int index4 = ((i+1) * 10 + j+1) * 3;

            if (j != 9) {
                glVertex3f(gridPoints[index1], gridPoints[index1+1], gridPoints[index1+2]);
                glVertex3f(gridPoints[index2], gridPoints[index2+1], gridPoints[index2+2]);
            }

            if (i != 9) {
                glVertex3f(gridPoints[index1], gridPoints[index1+1], gridPoints[index1+2]);
                glVertex3f(gridPoints[index3], gridPoints[index3+1], gridPoints[index3+2]);
            }
        }
    }
    glEnd();
}

// 窗口重绘回调函数
void display() {
    glClear(GL_COLOR_BUFFER_BIT | GL_DEPTH_BUFFER_BIT); // 清空颜色和深度缓冲区
    glLoadIdentity(); // 重置变换矩阵

    // 将曲面平移、旋转、缩放到合适位置
    glTranslatef(0.0f, 0.0f, -10.0f);
    glRotatef(30.0f, 1.0f, 0.0f, 0.0f);
    glRotatef(45.0f, 0.0f, 1.0f, 0.0f);
    glScalef(2.0f, 2.0f, 2.0f);

    drawBezierSurface(); // 绘制 Bezier 曲面

    glutSwapBuffers(); // 切换前后缓冲区，显示绘制结果
}

// 窗口大小改变回调函数
void reshape(int width, int height) {
    glViewport(0, 0, width, height); // 设置视口大小
    glMatrixMode(GL_PROJECTION); // 选择投影矩阵
    glLoadIdentity(); // 重置投影矩阵
    gluPerspective(60.0f, (float)width/height, 1.0f, 100.0f); // 设置投影矩阵
    glMatrixMode(GL_MODELVIEW); // 选择模型视图矩阵
}

// 鼠标移动回调函数
void mouseMove(int x, int y) {
    // 将鼠标坐标转换为 [-1, 1] 范围内的坐标
    float u = (float)x / WINDOW_WIDTH * 2.0f - 1.0f;
    float v = (float)(WINDOW_HEIGHT-y) / WINDOW_HEIGHT * 2.0f - 1.0f;

    // 遍历控制点数组，将鼠标附近的控制点位置改变一定值
    for (int i = 0; i < 16; i++) {
        int index = i * 3;
        float dx = controlPoints[index] - u;
        float dy = controlPoints[index+1] - v;
        float distance = sqrt(dx*dx + dy*dy);
        if (distance < 0.05f) {
            controlPoints[index] += dx * 0.1f;
            controlPoints[index+1] += dy * 0.1f;
        }
    }

    // 清空网格点数组，重新计算网格点坐标
    gridPoints.clear();
    for (float v = 0; v <= 1.0f; v += 0.1f) {
        for (float u = 0; u <= 1.0f; u += 0.1f) {
            vector<float> point = computePointOnSurface(u, v);
            gridPoints.push_back(point[0]);
            gridPoints.push_back(point[1]);
            gridPoints.push_back(point[2]);
        }
    }

    glutPostRedisplay(); // 标记窗口需要重绘
}

int main(int argc, char **argv) {
    glutInit(&argc, argv); // 初始化 GLUT 库
    glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB | GLUT_DEPTH); // 设置双缓冲、RGB 颜色模式和深度测试
    glutInitWindowSize(WINDOW_WIDTH, WINDOW_HEIGHT); // 设置窗口大小
    glutCreateWindow("Bezier Surface"); // 创建窗口并设置标题

    init(); // 初始化 OpenGL

    glutDisplayFunc(display); // 设置窗口重绘回调函数
    glutReshapeFunc(reshape); // 设置窗口大小改变回调函数
    glutPassiveMotionFunc(mouseMove); // 设置鼠标移动回调函数

    glEnable(GL_DEPTH_TEST); // 启用深度测试

    glutMainLoop(); // 进入事件循环，等待窗口事件发生

    return 0;
}

这个示例代码使用了 OpenGL 库来绘制 Bezier 曲面和网格，你需要在 Visual Studio 中添加 OpenGL 库的链接库和头文件，否则代码将无法编译。另外，示例代码中使用了鼠标移动事件来改变控制点位置，你需要在窗口显示时移动鼠标才能看到效果。