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：
1 import numpy as np 2 import matplotlib.pyplot as plt 3 import bezier 4 b_xs = [] 5 b_ys = [] 6 7 8 # xs表示原始数据 9 # n表示阶数 10 # k表示索引 11 def one_bezier_curve(a, b, t): 12 return (1 - t) * a + t * b 13 14 15 def n_bezier_curve(xs, n, k, t): 16 if n == 1: 17 return one_bezier_curve(xs[k], xs[k + 1], t) 18 else: 19 return (1 - t) * n_bezier_curve(xs, n - 1, k, t) + t * n_bezier_curve(xs, n - 1, k + 1, t) 20 21 22 def bezier_curve(xs, ys, num, b_xs, b_ys): 23 n = 5 # 采用5次bezier曲线拟合 24 t_step = 1.0 / (num - 1) 25 # t_step = 1.0 / num 26 print(t_step) 27 t = np.arange(0.0, 1 + t_step, t_step) 28 print(len(t)) 29 for each in t: 30 b_xs.append(n_bezier_curve(xs, n, 0, each)) 31 b_ys.append(n_bezier_curve(ys, n, 0, each)) 32 33 34 def func(): 35 xs = [1.0, 2.1, 3.0, 4.0, 5.0, 6.0] 36 ys = [0, 1.1, 2.1, 1.0, 0.2, 0] 37 num = 20 38 39 bezier_curve(xs, ys, num, b_xs, b_ys) # 将计算结果加入到列表中 40 print(b_xs, b_ys) 41 plt.figure() 42 plt.plot(b_xs, b_ys, 'r') # bezier曲线 43 # plt.plot(xs, ys) # 原曲线 44 # plt.show() 45 46 func()
2. 拼接bezier曲线
def point_bezier(avoid_point): global p xs = avoid_point[0, 0] # 0 ys = avoid_point[1, 0] # 0 xe = avoid_point[0, -1] # 34.5844 ye = avoid_point[1, -1] # 0 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）
1 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]]) 2 curve = bezier.Curve(a, degree=5) 3 # print(curve) 4 s_vals = np.linspace(0.0, 1.0, 30) 5 data = curve.evaluate_multi(s_vals) 6 x33 = data[0] 7 y33 = data[1] 8 plt.plot(x33, y33, 'y', linewidth=2.0, linestyle="-", label="y2") 9 plt.show()