c++生成一个B样条曲面代码

以下是一个简单的C++代码示例，用于生成一个B样条曲面。此处用到了OpenCV库中的cv::Mat类来保存图像数据，以及cv::Point3d类来表示三维坐标点。

#include <opencv2/opencv.hpp>
#include <vector>

using namespace cv;
using namespace std;

// 计算B样条基函数
double BsplineBasis(int i, int k, double u, vector<double> knots)
{
    if (k == 1)
    {
        if (u >= knots[i] && u < knots[i + 1])
        {
            return 1;
        }
        else
        {
            return 0;
        }
    }
    else
    {
        double w1 = 0, w2 = 0;
        if (knots[i + k - 1] - knots[i] != 0)
        {
            w1 = (u - knots[i]) / (knots[i + k - 1] - knots[i]) * BsplineBasis(i, k - 1, u, knots);
        }
        if (knots[i + k] - knots[i + 1] != 0)
        {
            w2 = (knots[i + k] - u) / (knots[i + k] - knots[i + 1]) * BsplineBasis(i + 1, k - 1, u, knots);
        }
        return w1 + w2;
    }
}

// 计算B样条曲面上指定点的坐标
Point3d BsplineSurfacePoint(double u, double v, vector<double> uknots, vector<double> vknots, vector<vector<Point3d>> controlPoints)
{
    int n = controlPoints.size() - 1;
    int m = controlPoints[0].size() - 1;
    Point3d result(0, 0, 0);
    for (int i = 0; i <= n; i++)
    {
        for (int j = 0; j <= m; j++)
        {
            double Bu = BsplineBasis(i, 4, u, uknots);
            double Bv = BsplineBasis(j, 4, v, vknots);
            result += controlPoints[i][j] * Bu * Bv;
        }
    }
    return result;
}

int main()
{
    int width = 640;
    int height = 480;
    Mat image(height, width, CV_8UC3, Scalar(0, 0, 0));

    // 定义B样条曲面控制点
    vector<vector<Point3d>> controlPoints = {
        {Point3d(0, 0, 0), Point3d(0, 1, 1), Point3d(0, 2, 1), Point3d(0, 3, 0)},
        {Point3d(1, 0, 1), Point3d(1, 1, 2), Point3d(1, 2, 2), Point3d(1, 3, 1)},
        {Point3d(2, 0, 1), Point3d(2, 1, 2), Point3d(2, 2, 2), Point3d(2, 3, 1)},
        {Point3d(3, 0, 0), Point3d(3, 1, 1), Point3d(3, 2, 1), Point3d(3, 3, 0)}
    };

    // 定义B样条曲面的参数
    vector<double> uknots = {0, 0, 0, 0, 1, 1, 1, 1};
    vector<double> vknots = {0, 0, 0, 0, 1, 1, 1, 1};
    double ustep = 0.1;
    double vstep = 0.1;

    // 在图像上绘制B样条曲面
    for (double u = 0; u <= 1; u += ustep)
    {
        for (double v = 0; v <= 1; v += vstep)
        {
            Point3d point = BsplineSurfacePoint(u, v, uknots, vknots, controlPoints);
            int x = point.x * 50 + width / 2;
            int y = -point.y * 50 + height / 2;
            circle(image, Point(x, y), 2, Scalar(255, 255, 255), -1);
        }
    }

    imshow("B-spline Surface", image);
    waitKey(0);
    return 0;
}

此代码绘制了一个简单的B样条曲面，并将其渲染到了一个OpenCV窗口中。该曲面由一个4x4的控制点矩阵定义，并使用了一个4阶B样条基函数。在绘制曲面时，使用了0.1的步长对曲面进行采样，并将采样点在图像上进行绘制。