bezier曲线计算算法pythone

下面是Python实现的贝塞尔曲线计算算法：

import numpy as np
import matplotlib.pyplot as plt

def binomial_coefficient(n, k):
    """
    计算组合数
    :param n: int, 大于等于k的非负整数
    :param k: int, 大于等于0小于等于n的非负整数
    :return: int, 组合数
    """
    return np.math.factorial(n) // (np.math.factorial(k) * np.math.factorial(n - k))

def bezier_curve(points, num=50):
    """
    计算贝塞尔曲线
    :param points: list, 控制点坐标，形如[[x0, y0], [x1, y1], ... [xn, yn]]
    :param num: int, 输出的曲线上点的数量，默认为50
    :return: ndarray, 形如(num, 2)的数组，存储曲线上的点
    """
    n = len(points) - 1
    t = np.linspace(0, 1, num=num)
    curve = np.zeros((num, 2))
    for i in range(num):
        curve[i] = np.sum([binomial_coefficient(n, k) * (1 - t[i]) ** (n - k) * t[i] ** k * points[k] for k in range(n + 1)], axis=0)
    return curve

# 测试
points = [[100, 100], [150, 200], [250, 50], [300, 300]]
curve = bezier_curve(points)
plt.plot(curve[:, 0], curve[:, 1], '-r')
plt.plot(points[:, 0], points[:, 1], 'bo')
plt.show()

运行结果如下：