我有一个由一系列(x,y)对组成的轨迹，我想使用样条插值在这个轨迹上插入点。
我该如何做？使用scipy.interpolate.UnivariateSpline无法实现，因为x和y都不是单调的。我可以引入参数化（例如沿轨迹的长度d），但那样我就有了两个相关变量x(d)和y(d)。
示例：
import numpy as np
import matplotlib.pyplot as plt
import math
error = 0.1
x0 = 1
y0 = 1
r0 = 0.5
alpha = np.linspace(0, 2*math.pi, 40, endpoint=False)
r = r0 + error * np.random.random(len(alpha))
x = x0 + r * np.cos(alpha)
y = x0 + r * np.sin(alpha)
plt.scatter(x, y, color='blue', label='given')
# For this special case, the following code produces the
# desired results. However, I need something that depends
# only on x and y:
from scipy.interpolate import interp1d
alpha_i = np.linspace(alpha[0], alpha[-1], 100)
r_i = interp1d(alpha, r, kind=3)(alpha_i)
x_i = x0 + r_i * np.cos(alpha_i)
y_i = x0 + r_i * np.sin(alpha_i)
plt.plot(x_i, y_i, color='green', label='desired')
plt.legend()
plt.show()
