将闭合曲线拟合到一组噪声点
fitting closed curve to a set of noisy points
这是我的数据集，我想在其中拟合一条闭合曲线，就像
array([[ 0.3 , -0.05],
[ 0.35, -0.05],
[ 0.4 , -0.05],
[ 0.45, -0.05],
[ 0.5 , -0.05],
[ 0.55, -0.05],
[ 0.6 , -0.05],
[ 0.65, -0.05],
[ 0.7 , -0.05],
[ 0.75, -0.05],
[ 0.8 , -0.05],
[ 0.85, -0.05],
[ 0.9 , -0.05],
[ 0.95, -0.05],
[ 1. , -0.05],
[ 1.05, -0.05],
[ 1.1 , -0.05],
[ 1.15, -0.05],
[ 1.2 , -0.05],
[ 1.25, -0.05],
[ 1.3 , -0.05],
[ 1.35, -0.05],
[ 1.4 , -0.05],
[ 1.45, -0.05],
[ 1.5 , -0.05],
[ 1.55, -0.05],
[ 1.6 , -0.05],
[ 1.65, -0.05],
[ 1.7 , -0.05],
[ 1.75, -0.05],
[ 1.8 , -0.05],
[ 0. , -0.1 ],
[ 0.05, -0.1 ],
[ 0. , -0.15],
[ 2.1 , -0.15],
[ 2.15, -0.15],
[ 0. , -0.2 ],
[ 2.1 , -0.2 ],
[ 2.15, -0.2 ],
[ 2.2 , -0.2 ],
[ 2.2 , -0.25],
[ 2.35, -0.35],
[-0.15, -0.4 ],
[ 2.35, -0.4 ],
[-0.15, -0.45],
[ 2.35, -0.45],
[ 2.4 , -0.45],
[ 2.35, -0.5 ],
[ 2.4 , -0.5 ],
[ 2.4 , -0.55],
[-0.25, -0.6 ],
[-0.2 , -0.6 ],
[ 2.4 , -0.6 ],
[ 2.45, -0.6 ],
[-0.4 , -0.65],
[ 2.45, -0.65],
[-0.4 , -0.7 ],
[ 2.45, -0.7 ],
[ 2.5 , -0.7 ],
[ 2.45, -0.75],
[ 2.45, -0.8 ],
[-0.5 , -0.85],
[ 2.45, -0.85],
[ 2.5 , -0.85],
[-0.5 , -0.9 ],
[ 2.45, -0.9 ],
[ 2.5 , -0.9 ],
[-0.5 , -0.95],
[ 2.5 , -0.95],
[-0.5 , -1. ],
[ 2.5 , -1. ],
[-0.5 , -1.05],
[-0.45, -1.05],
[ 2.5 , -1.05],
[-0.5 , -1.1 ],
[-0.45, -1.1 ],
[ 2.5 , -1.1 ],
[ 2.55, -1.1 ],
[-0.5 , -1.15],
[-0.45, -1.15],
[ 2.5 , -1.15],
[ 2.55, -1.15],
[-0.5 , -1.2 ],
[-0.45, -1.2 ],
[ 2.5 , -1.2 ],
[ 2.55, -1.2 ],
[-0.45, -1.25],
[ 2.55, -1.25],
[-0.45, -1.3 ],
[ 2.55, -1.3 ],
[-0.45, -1.35],
[ 2.55, -1.35],
[-0.45, -1.4 ],
[ 2.55, -1.4 ],
[-0.45, -1.45],
[-0.4 , -1.45],
[ 2.55, -1.45],
[-0.45, -1.5 ],
[-0.4 , -1.5 ],
[ 2.6 , -1.5 ],
[-0.45, -1.55],
[-0.4 , -1.55],
[ 2.6 , -1.55],
[-0.45, -1.6 ],
[-0.4 , -1.6 ],
[ 2.6 , -1.6 ],
[-0.45, -1.65],
[-0.4 , -1.65],
[ 2.6 , -1.65],
[-0.45, -1.7 ],
[-0.4 , -1.7 ],
[ 2.6 , -1.7 ],
[-0.4 , -1.75],
[ 2.55, -1.75],
[-0.4 , -1.8 ],
[ 2.55, -1.8 ],
[-0.45, -1.85],
[-0.4 , -1.85],
[ 2.55, -1.85],
[-0.45, -1.9 ],
[-0.4 , -1.9 ],
[-0.4 , -1.95],
[-0.4 , -2. ],
[-0.35, -2. ],
[-0.4 , -2.05],
[-0.35, -2.05],
[ 2.5 , -2.05],
[ 2.55, -2.05],
[-0.35, -2.1 ],
[ 2.5 , -2.1 ],
[ 2.55, -2.1 ],
[-0.35, -2.15],
[ 2.5 , -2.15],
[ 2.55, -2.15],
[-0.4 , -2.2 ],
[-0.35, -2.2 ],
[ 2.5 , -2.2 ],
[-0.4 , -2.25],
[-0.35, -2.25],
[-0.35, -2.3 ],
[ 2.45, -2.3 ],
[-0.3 , -2.35],
[ 2.45, -2.35],
[-0.3 , -2.4 ],
[-0.3 , -2.45],
[-0.2 , -2.6 ],
[ 2.05, -2.6 ],
[ 2.2 , -2.6 ],
[ 2.25, -2.6 ],
[ 2.1 , -2.65],
[-0.15, -2.7 ],
[-0.05, -2.75],
[ 0. , -2.75],
[ 0.05, -2.75],
[ 0.1 , -2.75],
[ 0.15, -2.75],
[-0.05, -2.8 ],
[ 0. , -2.8 ],
[ 0.05, -2.8 ],
[ 0.1 , -2.8 ],
[ 1.1 , -2.8 ],
[ 1.15, -2.8 ],
[ 1.2 , -2.8 ],
[ 1.25, -2.8 ],
[ 1.3 , -2.8 ],
[ 1.35, -2.8 ],
[ 1.4 , -2.8 ],
[ 1.45, -2.8 ],
[ 1.5 , -2.8 ],
[ 1.55, -2.8 ],
[ 1.6 , -2.8 ],
[ 1.65, -2.8 ],
[ 1.7 , -2.8 ],
[ 1.75, -2.8 ],
[ 1.8 , -2.8 ],
[ 0.7 , -2.85],
[ 0.75, -2.85],
[ 0.8 , -2.85],
[ 0.85, -2.85],
[ 0.9 , -2.85],
[ 0.95, -2.85],
[ 1. , -2.85],
[ 1.05, -2.85]])
这是可视化数据集：
但是，无论我如何对数组进行排序，这些都是我得到的结果。
我提出了一些关于我的数据集的问题，但不知道如何处理它们：
- 许多 x 和 y 值不是一一对应的
- 点未按相邻顺序排序
因此，如果我的假设是正确的，那么主要问题将是如何按照 splprep 方法起作用的顺序对数组进行排序？如果没有，我将非常感谢任何能帮助我解决问题的解决方案！
[更新]感谢@michael-szczesny的回复我得到了一个满意的结果
您可以将数据平移到原点并按复角排序。
设置数据
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import splprep, splev
x = np.array(
[[-0.50, -1.20],
[-0.50, -1.15],
[-0.50, -1.10],
[-0.50, -1.05],
[-0.50, -1.00],
[-0.50, -0.95],
[-0.50, -0.90],
[-0.50, -0.85],
[-0.45, -1.90],
[-0.45, -1.85],
[-0.45, -1.70],
[-0.45, -1.65],
[-0.45, -1.60],
[-0.45, -1.55],
[-0.45, -1.50],
[-0.45, -1.45],
[-0.45, -1.40],
[-0.45, -1.35],
[-0.45, -1.30],
[-0.45, -1.25],
[-0.45, -1.20],
[-0.45, -1.15],
[-0.45, -1.10],
[-0.45, -1.05],
[-0.40, -2.25],
[-0.40, -2.20],
[-0.40, -2.05],
[-0.40, -2.00],
[-0.40, -1.95],
[-0.40, -1.90],
[-0.40, -1.85],
[-0.40, -1.80],
[-0.40, -1.75],
[-0.40, -1.70],
[-0.40, -1.65],
[-0.40, -1.60],
[-0.40, -1.55],
[-0.40, -1.50],
[-0.40, -1.45],
[-0.40, -0.70],
[-0.40, -0.65],
[-0.35, -2.30],
[-0.35, -2.25],
[-0.35, -2.20],
[-0.35, -2.15],
[-0.35, -2.10],
[-0.35, -2.05],
[-0.35, -2.00],
[-0.30, -2.45],
[-0.30, -2.40],
[-0.30, -2.35],
[-0.25, -0.60],
[-0.20, -2.60],
[-0.20, -0.60],
[-0.15, -2.70],
[-0.15, -0.45],
[-0.15, -0.40],
[-0.05, -2.80],
[-0.05, -2.75],
[0.00, -2.80],
[0.00, -2.75],
[0.00, -0.20],
[0.00, -0.15],
[0.00, -0.10],
[0.05, -2.80],
[0.05, -2.75],
[0.05, -0.10],
[0.10, -2.80],
[0.10, -2.75],
[0.15, -2.75],
[0.30, -0.05],
[0.35, -0.05],
[0.40, -0.05],
[0.45, -0.05],
[0.50, -0.05],
[0.55, -0.05],
[0.60, -0.05],
[0.65, -0.05],
[0.70, -2.85],
[0.70, -0.05],
[0.75, -2.85],
[0.75, -0.05],
[0.80, -2.85],
[0.80, -0.05],
[0.85, -2.85],
[0.85, -0.05],
[0.90, -2.85],
[0.90, -0.05],
[0.95, -2.85],
[0.95, -0.05],
[1.00, -2.85],
[1.00, -0.05],
[1.05, -2.85],
[1.05, -0.05],
[1.10, -2.80],
[1.10, -0.05],
[1.15, -2.80],
[1.15, -0.05],
[1.20, -2.80],
[1.20, -0.05],
[1.25, -2.80],
[1.25, -0.05],
[1.30, -2.80],
[1.30, -0.05],
[1.35, -2.80],
[1.35, -0.05],
[1.40, -2.80],
[1.40, -0.05],
[1.45, -2.80],
[1.45, -0.05],
[1.50, -2.80],
[1.50, -0.05],
[1.55, -2.80],
[1.55, -0.05],
[1.60, -2.80],
[1.60, -0.05],
[1.65, -2.80],
[1.65, -0.05],
[1.70, -2.80],
[1.70, -0.05],
[1.75, -2.80],
[1.75, -0.05],
[1.80, -2.80],
[1.80, -0.05],
[2.05, -2.60],
[2.10, -2.65],
[2.10, -0.20],
[2.10, -0.15],
[2.15, -0.20],
[2.15, -0.15],
[2.20, -2.60],
[2.20, -0.25],
[2.20, -0.20],
[2.25, -2.60],
[2.35, -0.50],
[2.35, -0.45],
[2.35, -0.40],
[2.35, -0.35],
[2.40, -0.60],
[2.40, -0.55],
[2.40, -0.50],
[2.40, -0.45],
[2.45, -2.35],
[2.45, -2.30],
[2.45, -0.90],
[2.45, -0.85],
[2.45, -0.80],
[2.45, -0.75],
[2.45, -0.70],
[2.45, -0.65],
[2.45, -0.60],
[2.50, -2.20],
[2.50, -2.15],
[2.50, -2.10],
[2.50, -2.05],
[2.50, -1.20],
[2.50, -1.15],
[2.50, -1.10],
[2.50, -1.05],
[2.50, -1.00],
[2.50, -0.95],
[2.50, -0.90],
[2.50, -0.85],
[2.50, -0.70],
[2.55, -2.15],
[2.55, -2.10],
[2.55, -2.05],
[2.55, -1.85],
[2.55, -1.80],
[2.55, -1.75],
[2.55, -1.45],
[2.55, -1.40],
[2.55, -1.35],
[2.55, -1.30],
[2.55, -1.25],
[2.55, -1.20],
[2.55, -1.15],
[2.55, -1.10],
[2.60, -1.70],
[2.60, -1.65],
[2.60, -1.60],
[2.60, -1.55],
[2.60, -1.50]])
使用 np.angle((xs[:,0] + 1j*xs[:,1])) 将您的数据转换为复数坐标，并使用它对您的数据进行排序。
xs = (x - x.mean(0))
x_sort = xs[np.angle((xs[:,0] + 1j*xs[:,1])).argsort()]
现在您可以 (code by @rth) 以正确的顺序排列您的数据。
# plot from as mentioned in the question
tck, u = splprep(x_sort.T, u=None, s=0.0, per=1)
u_new = np.linspace(u.min(), u.max(), 1000)
x_new, y_new = splev(u_new, tck, der=0)
plt.figure(figsize=(10,10))
plt.plot(x_sort[:,0], x_sort[:,1], 'ro')
plt.plot(x_new, y_new, 'b--');
输出：
这是我的数据集，我想在其中拟合一条闭合曲线，就像
array([[ 0.3 , -0.05],
[ 0.35, -0.05],
[ 0.4 , -0.05],
[ 0.45, -0.05],
[ 0.5 , -0.05],
[ 0.55, -0.05],
[ 0.6 , -0.05],
[ 0.65, -0.05],
[ 0.7 , -0.05],
[ 0.75, -0.05],
[ 0.8 , -0.05],
[ 0.85, -0.05],
[ 0.9 , -0.05],
[ 0.95, -0.05],
[ 1. , -0.05],
[ 1.05, -0.05],
[ 1.1 , -0.05],
[ 1.15, -0.05],
[ 1.2 , -0.05],
[ 1.25, -0.05],
[ 1.3 , -0.05],
[ 1.35, -0.05],
[ 1.4 , -0.05],
[ 1.45, -0.05],
[ 1.5 , -0.05],
[ 1.55, -0.05],
[ 1.6 , -0.05],
[ 1.65, -0.05],
[ 1.7 , -0.05],
[ 1.75, -0.05],
[ 1.8 , -0.05],
[ 0. , -0.1 ],
[ 0.05, -0.1 ],
[ 0. , -0.15],
[ 2.1 , -0.15],
[ 2.15, -0.15],
[ 0. , -0.2 ],
[ 2.1 , -0.2 ],
[ 2.15, -0.2 ],
[ 2.2 , -0.2 ],
[ 2.2 , -0.25],
[ 2.35, -0.35],
[-0.15, -0.4 ],
[ 2.35, -0.4 ],
[-0.15, -0.45],
[ 2.35, -0.45],
[ 2.4 , -0.45],
[ 2.35, -0.5 ],
[ 2.4 , -0.5 ],
[ 2.4 , -0.55],
[-0.25, -0.6 ],
[-0.2 , -0.6 ],
[ 2.4 , -0.6 ],
[ 2.45, -0.6 ],
[-0.4 , -0.65],
[ 2.45, -0.65],
[-0.4 , -0.7 ],
[ 2.45, -0.7 ],
[ 2.5 , -0.7 ],
[ 2.45, -0.75],
[ 2.45, -0.8 ],
[-0.5 , -0.85],
[ 2.45, -0.85],
[ 2.5 , -0.85],
[-0.5 , -0.9 ],
[ 2.45, -0.9 ],
[ 2.5 , -0.9 ],
[-0.5 , -0.95],
[ 2.5 , -0.95],
[-0.5 , -1. ],
[ 2.5 , -1. ],
[-0.5 , -1.05],
[-0.45, -1.05],
[ 2.5 , -1.05],
[-0.5 , -1.1 ],
[-0.45, -1.1 ],
[ 2.5 , -1.1 ],
[ 2.55, -1.1 ],
[-0.5 , -1.15],
[-0.45, -1.15],
[ 2.5 , -1.15],
[ 2.55, -1.15],
[-0.5 , -1.2 ],
[-0.45, -1.2 ],
[ 2.5 , -1.2 ],
[ 2.55, -1.2 ],
[-0.45, -1.25],
[ 2.55, -1.25],
[-0.45, -1.3 ],
[ 2.55, -1.3 ],
[-0.45, -1.35],
[ 2.55, -1.35],
[-0.45, -1.4 ],
[ 2.55, -1.4 ],
[-0.45, -1.45],
[-0.4 , -1.45],
[ 2.55, -1.45],
[-0.45, -1.5 ],
[-0.4 , -1.5 ],
[ 2.6 , -1.5 ],
[-0.45, -1.55],
[-0.4 , -1.55],
[ 2.6 , -1.55],
[-0.45, -1.6 ],
[-0.4 , -1.6 ],
[ 2.6 , -1.6 ],
[-0.45, -1.65],
[-0.4 , -1.65],
[ 2.6 , -1.65],
[-0.45, -1.7 ],
[-0.4 , -1.7 ],
[ 2.6 , -1.7 ],
[-0.4 , -1.75],
[ 2.55, -1.75],
[-0.4 , -1.8 ],
[ 2.55, -1.8 ],
[-0.45, -1.85],
[-0.4 , -1.85],
[ 2.55, -1.85],
[-0.45, -1.9 ],
[-0.4 , -1.9 ],
[-0.4 , -1.95],
[-0.4 , -2. ],
[-0.35, -2. ],
[-0.4 , -2.05],
[-0.35, -2.05],
[ 2.5 , -2.05],
[ 2.55, -2.05],
[-0.35, -2.1 ],
[ 2.5 , -2.1 ],
[ 2.55, -2.1 ],
[-0.35, -2.15],
[ 2.5 , -2.15],
[ 2.55, -2.15],
[-0.4 , -2.2 ],
[-0.35, -2.2 ],
[ 2.5 , -2.2 ],
[-0.4 , -2.25],
[-0.35, -2.25],
[-0.35, -2.3 ],
[ 2.45, -2.3 ],
[-0.3 , -2.35],
[ 2.45, -2.35],
[-0.3 , -2.4 ],
[-0.3 , -2.45],
[-0.2 , -2.6 ],
[ 2.05, -2.6 ],
[ 2.2 , -2.6 ],
[ 2.25, -2.6 ],
[ 2.1 , -2.65],
[-0.15, -2.7 ],
[-0.05, -2.75],
[ 0. , -2.75],
[ 0.05, -2.75],
[ 0.1 , -2.75],
[ 0.15, -2.75],
[-0.05, -2.8 ],
[ 0. , -2.8 ],
[ 0.05, -2.8 ],
[ 0.1 , -2.8 ],
[ 1.1 , -2.8 ],
[ 1.15, -2.8 ],
[ 1.2 , -2.8 ],
[ 1.25, -2.8 ],
[ 1.3 , -2.8 ],
[ 1.35, -2.8 ],
[ 1.4 , -2.8 ],
[ 1.45, -2.8 ],
[ 1.5 , -2.8 ],
[ 1.55, -2.8 ],
[ 1.6 , -2.8 ],
[ 1.65, -2.8 ],
[ 1.7 , -2.8 ],
[ 1.75, -2.8 ],
[ 1.8 , -2.8 ],
[ 0.7 , -2.85],
[ 0.75, -2.85],
[ 0.8 , -2.85],
[ 0.85, -2.85],
[ 0.9 , -2.85],
[ 0.95, -2.85],
[ 1. , -2.85],
[ 1.05, -2.85]])
这是可视化数据集：
我提出了一些关于我的数据集的问题，但不知道如何处理它们：
- 许多 x 和 y 值不是一一对应的
- 点未按相邻顺序排序
因此，如果我的假设是正确的，那么主要问题将是如何按照 splprep 方法起作用的顺序对数组进行排序？如果没有，我将非常感谢任何能帮助我解决问题的解决方案！
[更新]感谢@michael-szczesny的回复我得到了一个满意的结果
您可以将数据平移到原点并按复角排序。
设置数据
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import splprep, splev
x = np.array(
[[-0.50, -1.20],
[-0.50, -1.15],
[-0.50, -1.10],
[-0.50, -1.05],
[-0.50, -1.00],
[-0.50, -0.95],
[-0.50, -0.90],
[-0.50, -0.85],
[-0.45, -1.90],
[-0.45, -1.85],
[-0.45, -1.70],
[-0.45, -1.65],
[-0.45, -1.60],
[-0.45, -1.55],
[-0.45, -1.50],
[-0.45, -1.45],
[-0.45, -1.40],
[-0.45, -1.35],
[-0.45, -1.30],
[-0.45, -1.25],
[-0.45, -1.20],
[-0.45, -1.15],
[-0.45, -1.10],
[-0.45, -1.05],
[-0.40, -2.25],
[-0.40, -2.20],
[-0.40, -2.05],
[-0.40, -2.00],
[-0.40, -1.95],
[-0.40, -1.90],
[-0.40, -1.85],
[-0.40, -1.80],
[-0.40, -1.75],
[-0.40, -1.70],
[-0.40, -1.65],
[-0.40, -1.60],
[-0.40, -1.55],
[-0.40, -1.50],
[-0.40, -1.45],
[-0.40, -0.70],
[-0.40, -0.65],
[-0.35, -2.30],
[-0.35, -2.25],
[-0.35, -2.20],
[-0.35, -2.15],
[-0.35, -2.10],
[-0.35, -2.05],
[-0.35, -2.00],
[-0.30, -2.45],
[-0.30, -2.40],
[-0.30, -2.35],
[-0.25, -0.60],
[-0.20, -2.60],
[-0.20, -0.60],
[-0.15, -2.70],
[-0.15, -0.45],
[-0.15, -0.40],
[-0.05, -2.80],
[-0.05, -2.75],
[0.00, -2.80],
[0.00, -2.75],
[0.00, -0.20],
[0.00, -0.15],
[0.00, -0.10],
[0.05, -2.80],
[0.05, -2.75],
[0.05, -0.10],
[0.10, -2.80],
[0.10, -2.75],
[0.15, -2.75],
[0.30, -0.05],
[0.35, -0.05],
[0.40, -0.05],
[0.45, -0.05],
[0.50, -0.05],
[0.55, -0.05],
[0.60, -0.05],
[0.65, -0.05],
[0.70, -2.85],
[0.70, -0.05],
[0.75, -2.85],
[0.75, -0.05],
[0.80, -2.85],
[0.80, -0.05],
[0.85, -2.85],
[0.85, -0.05],
[0.90, -2.85],
[0.90, -0.05],
[0.95, -2.85],
[0.95, -0.05],
[1.00, -2.85],
[1.00, -0.05],
[1.05, -2.85],
[1.05, -0.05],
[1.10, -2.80],
[1.10, -0.05],
[1.15, -2.80],
[1.15, -0.05],
[1.20, -2.80],
[1.20, -0.05],
[1.25, -2.80],
[1.25, -0.05],
[1.30, -2.80],
[1.30, -0.05],
[1.35, -2.80],
[1.35, -0.05],
[1.40, -2.80],
[1.40, -0.05],
[1.45, -2.80],
[1.45, -0.05],
[1.50, -2.80],
[1.50, -0.05],
[1.55, -2.80],
[1.55, -0.05],
[1.60, -2.80],
[1.60, -0.05],
[1.65, -2.80],
[1.65, -0.05],
[1.70, -2.80],
[1.70, -0.05],
[1.75, -2.80],
[1.75, -0.05],
[1.80, -2.80],
[1.80, -0.05],
[2.05, -2.60],
[2.10, -2.65],
[2.10, -0.20],
[2.10, -0.15],
[2.15, -0.20],
[2.15, -0.15],
[2.20, -2.60],
[2.20, -0.25],
[2.20, -0.20],
[2.25, -2.60],
[2.35, -0.50],
[2.35, -0.45],
[2.35, -0.40],
[2.35, -0.35],
[2.40, -0.60],
[2.40, -0.55],
[2.40, -0.50],
[2.40, -0.45],
[2.45, -2.35],
[2.45, -2.30],
[2.45, -0.90],
[2.45, -0.85],
[2.45, -0.80],
[2.45, -0.75],
[2.45, -0.70],
[2.45, -0.65],
[2.45, -0.60],
[2.50, -2.20],
[2.50, -2.15],
[2.50, -2.10],
[2.50, -2.05],
[2.50, -1.20],
[2.50, -1.15],
[2.50, -1.10],
[2.50, -1.05],
[2.50, -1.00],
[2.50, -0.95],
[2.50, -0.90],
[2.50, -0.85],
[2.50, -0.70],
[2.55, -2.15],
[2.55, -2.10],
[2.55, -2.05],
[2.55, -1.85],
[2.55, -1.80],
[2.55, -1.75],
[2.55, -1.45],
[2.55, -1.40],
[2.55, -1.35],
[2.55, -1.30],
[2.55, -1.25],
[2.55, -1.20],
[2.55, -1.15],
[2.55, -1.10],
[2.60, -1.70],
[2.60, -1.65],
[2.60, -1.60],
[2.60, -1.55],
[2.60, -1.50]])
使用 np.angle((xs[:,0] + 1j*xs[:,1])) 将您的数据转换为复数坐标，并使用它对您的数据进行排序。
xs = (x - x.mean(0))
x_sort = xs[np.angle((xs[:,0] + 1j*xs[:,1])).argsort()]
现在您可以
# plot from as mentioned in the question
tck, u = splprep(x_sort.T, u=None, s=0.0, per=1)
u_new = np.linspace(u.min(), u.max(), 1000)
x_new, y_new = splev(u_new, tck, der=0)
plt.figure(figsize=(10,10))
plt.plot(x_sort[:,0], x_sort[:,1], 'ro')
plt.plot(x_new, y_new, 'b--');
输出：