双三次bezier曲面片代码

以下是一个简单的双三次Bezier曲面片的实现代码示例：

#include <iostream>
using namespace std;

const int N = 4; // 控制点矩阵大小

struct Point {
    float x, y, z;
};

Point controlPoints[N][N]; // 控制点矩阵

// 计算组合数
int binomialCoeff(int n, int k) {
    int res = 1;
    if (k > n - k)
        k = n - k;
    for (int i = 0; i < k; ++i) {
        res *= (n - i);
        res /= (i + 1);
    }
    return res;
}

// 计算Bezier曲线上的点
Point bezierCurvePoint(Point* points, int n, float t) {
    Point res = { 0, 0, 0 };
    for (int i = 0; i < n; i++) {
        float coeff = binomialCoeff(n - 1, i) * pow(t, i) * pow(1 - t, n - 1 - i);
        res.x += points[i].x * coeff;
        res.y += points[i].y * coeff;
        res.z += points[i].z * coeff;
    }
    return res;
}

// 计算Bezier曲面上的点
Point bezierSurfacePoint(Point points[N][N], float u, float v) {
    Point uCurvePoints[N], vCurvePoints[N];
    for (int i = 0; i < N; i++) {
        Point rowPoints[N];
        for (int j = 0; j < N; j++) {
            rowPoints[j] = points[i][j];
        }
        uCurvePoints[i] = bezierCurvePoint(rowPoints, N, u);
    }
    for (int i = 0; i < N; i++) {
        Point colPoints[N];
        for (int j = 0; j < N; j++) {
            colPoints[j] = points[j][i];
        }
        vCurvePoints[i] = bezierCurvePoint(colPoints, N, v);
    }
    return bezierCurvePoint(uCurvePoints, N, v);
}

int main() {
    // 初始化控制点矩阵
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            controlPoints[i][j] = { i * 10.0f, j * 10.0f, i * j };
        }
    }

    // 计算曲面上的点
    Point point = bezierSurfacePoint(controlPoints, 0.3f, 0.6f);

    cout << "Point on Bezier Surface: (" << point.x << ", " << point.y << ", " << point.z << ")" << endl;

    return 0;
}

该代码示例中，我们定义了一个 `Point` 结构体来表示点，使用一个 `N*N` 的二维数组来存储控制点，其中 `N` 表示控制点矩阵的大小。`binomialCoeff` 函数用于计算组合数，`bezierCurvePoint` 函数用于计算Bezier曲线上的点，`bezierSurfacePoint` 函数用于计算Bezier曲面上的点。

在 `main` 函数中，我们首先初始化了控制点矩阵，然后调用 `bezierSurfacePoint` 函数计算曲面上的点，并输出结果。