csci/compute/bessel.cpp

#include "bessel.h"

vector<Point> Bessel::run(const vector<Point> &points, double step) {
    vector<Point> res;
    for (float t = 0; t <= 1; t += step) {
        Point p = bezier_curve(points, t);
        res.push_back(p);
    }
    return res;
}

// 计算n次贝塞尔曲线上的点
Point Bessel::bezier_curve(const vector<Point> &points, double t) {
    int n = points.size() - 1;
    Point res;
    for (int i = 0; i <= n; ++i) {
        double b =  binomial(n, i)* pow(t, i) * pow(1 - t, n - i);
        res.x = res.x + points[i].x * b;
        res.y = res.y + points[i].y * b;
        res.z = res.z + points[i].z * b;
    }
    return res;
}

// 计算组合数
int Bessel::binomial(int n, int i) {
    int res = 1;
    for (int j = 1; j <= i; ++j) {
        res *= (n - j + 1) / (double)j; //(double)十分关键，不然j=i=n时，j为分数=0；
    }
    return res;
}