python bezier 曲线

1.手写bezier公式，生成bezier代码, 如果给的点数过多，则会生成一半bezier曲线，剩下的一半就需要进行拼接：

 import numpy as np
 import matplotlib.pyplot as plt
 import bezier
 b_xs = []
 b_ys = []

 # xs表示原始数据
 # n表示阶数
 # k表示索引
 def one_bezier_curve(a, b, t):
     return (1 - t) * a + t * b

 def n_bezier_curve(xs, n, k, t):
     if n == 1:
         return one_bezier_curve(xs[k], xs[k + 1], t)
     else:
         return (1 - t) * n_bezier_curve(xs, n - 1, k, t) + t * n_bezier_curve(xs, n - 1, k + 1, t)

 def bezier_curve(xs, ys, num, b_xs, b_ys):
     n = 5  # 采用5次bezier曲线拟合
     t_step = 1.0 / (num - 1)
     # t_step = 1.0 / num
     print(t_step)
     t = np.arange(0.0, 1 + t_step, t_step)
     print(len(t))
     for each in t:
         b_xs.append(n_bezier_curve(xs, n, 0, each))
         b_ys.append(n_bezier_curve(ys, n, 0, each))

 def func():
     xs = [1.0, 2.1, 3.0, 4.0, 5.0, 6.0]
     ys = [0, 1.1, 2.1, 1.0, 0.2, 0]
     num = 20

     bezier_curve(xs, ys, num, b_xs, b_ys)  # 将计算结果加入到列表中
     print(b_xs, b_ys)
     plt.figure()
     plt.plot(b_xs, b_ys, 'r')  # bezier曲线
     # plt.plot(xs, ys)  # 原曲线
     # plt.show()

 func()

2. 拼接bezier曲线

def point_bezier(avoid_point):
    global p
    xs = avoid_point[0, 0]  #
    ys = avoid_point[1, 0]  #
    xe = avoid_point[0, -1]  # 34.5844
    ye = avoid_point[1, -1]  #
    Latoff = 2.3
    startp = np.array([xs, ys])
    endp = np.array([xe, ye])
    endp1 = np.array([xe+2, ye])
    # print(startp, endp)
    P0 = startp
    P1 = np.array([startp[0] + (endp[0] - startp[0]) / 8, startp[1]])
    P2 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 2, startp[1]])
    P3 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 2, startp[1] + Latoff])
    P4 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 3, startp[1] + Latoff])
    P5 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 4, startp[1] + Latoff])
    P6 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 5, startp[1] + Latoff])
    P7 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 6, startp[1] + Latoff])
    P8 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 6, startp[1] + Latoff])
    P9 = np.array([startp[0] + (endp[0] - startp[0]) / 8 * 7, startp[1]])
    P10 = endp
    P11 = endp1
    i = 1
    half_length = 0.5 * (xe + xs)
    for u in np.arange(startp[0], startp[0] + (endp[0] - startp[0]) / 2, 0.2):
        # for u =startp[0]:0.2: startp[1] + (endp[1] - startp[1]) / 2
        c = (1 - (u - startp[0]) / half_length) ** 5 * P0 + 5 * (1 - (u - startp[0]) / half_length) ** 4 * (
                u - startp[0]) / half_length * P1 + 10 * (1 - (u - startp[0]) / half_length) ** 3 * (
                    (u - startp[0]) / half_length) ** 2 * P2 + 10 * (1 - (u - startp[0]) / half_length) ** 2 * (
                    (u - startp[0]) / half_length) ** 3 * P3 + 5 * (1 - (u - startp[0]) / half_length) * (
                    (u - startp[0]) / half_length) ** 4 * P4 + ((u - startp[0]) / half_length) ** 5 * P5
        i = i + 1
        p = np.append(p, [c], axis=0)

    for u in np.arange(startp[0] + half_length, endp[0], 0.2):
        d = (1 - (u - startp[0] - half_length) / half_length) ** 5 * P6 + 5 * (
                    1 - (u - startp[0] - half_length) / half_length) ** 4 * (
                    u - startp[0] - half_length) / half_length * P7 + 10 * (
                        1 - (u - startp[0] - half_length) / half_length) ** 3 * (
                    (u - startp[0] - half_length) / half_length) ** 2 * P8 + 10 * (
                        1 - (u - startp[0] - half_length) / half_length) ** 2 * (
                    (u - startp[0] - half_length) / half_length) ** 3 * P9 + 5 * (
                        1 - (u - startp[0] - half_length) / half_length) * (
                    (u - startp[0] - half_length) / half_length) ** 4 * P10 + (
                        (u - startp[0] - half_length) / half_length) ** 5 * P11
        i = i + 1
        p = np.append(p, [d], axis=0)
    return p
    # print(p)
    # plt.plot(p[:, 0], p[:, 1], 'r')
    # plt.show()

3.使用python 内置bezier包，完成bezier曲线（使用前需安装bezier包）

 a = np.array([[1.0, 2.1, 3.0, 4.0, 5.0, 6.0], [0, 1.1, 2.1, 1.0, 0.2, 0]])
 curve = bezier.Curve(a, degree=5)
 # print(curve)
 s_vals = np.linspace(0.0, 1.0, 30)
 data = curve.evaluate_multi(s_vals)
 x33 = data[0]
 y33 = data[1]
 plt.plot(x33, y33, 'y', linewidth=2.0, linestyle="-", label="y2")
 plt.show()