拟合贝塞尔曲线c++代码

以下是一份C++版本的拟合贝塞尔曲线代码，可以实现二次和三次bezier曲线的绘制，具体实现方法和参数可以参考代码注释：

#include <iostream>
#include <vector>
#include <cmath>

using namespace std;

// 定义点的结构体
struct Point {
    double x;
    double y;
};

// 计算组合数C(n, i)
double Combination(int n, int i) {
    double res = 1;
    for (int j = 1; j <= i; j++) {
        res *= (n - j + 1) / (double)j;
    }
    return res;
}

// 计算贝塞尔曲线上某一点的坐标
Point Bezier(vector<Point>& points, double t) {
    int n = points.size() - 1;
    double x = 0, y = 0;
    for (int i = 0; i <= n; i++) {
        double factor = Combination(n, i) * pow(t, i) * pow(1 - t, n - i);
        x += factor * points[i].x;
        y += factor * points[i].y;
    }
    return { x, y };
}

// 拟合二次贝塞尔曲线
vector<Point> FitQuadraticBezier(vector<Point>& points) {
    vector<Point> res;
    if (points.size() < 3) {
        return res;
    }
    for (double t = 0; t <= 1; t += 0.01) {
        Point p = Bezier(points, t);
        res.push_back(p);
    }
    return res;
}

// 拟合三次贝塞尔曲线
vector<Point> FitCubicBezier(vector<Point>& points) {
    vector<Point> res;
    if (points.size() < 4) {
        return res;
    }
    for (double t = 0; t <= 1; t += 0.01) {
        Point p = Bezier(points, t);
        res.push_back(p);
    }
    return res;
}

int main() {
    // 示例：二阶贝塞尔曲线points = {{10,10}, {20, 80},{40,120}}
    vector<Point> points = { {10,10}, {20, 80},{40,120} };
    vector<Point> res = FitQuadraticBezier(points);
    for (auto p : res) {
        cout << "(" << p.x << ", " << p.y << ")" << endl;
    }
    return 0;
}