使用 Python 进行参数曲线拟合答案

【问题标题】：Parametric Curve Fitting Using Python使用 Python 进行参数曲线拟合
【发布时间】：2021-10-01 18:40:59
【问题描述】：

我想将参数曲线与一组点进行最佳拟合。曲线的起点和终点应分别与第一个和最后一个采样点重合。

我在下面尝试过这段代码，但它给了我一个闭合曲线。有没有办法稍微修改这段代码以确保曲线不闭合？

import numpy as np
from scipy import interpolate
from matplotlib import pyplot as plt

x = np.array([23, 24, 24, 25, 25])
y = np.array([13, 12, 13, 12, 13])

# append the starting x,y coordinates
x = np.r_[x, x[0]]
y = np.r_[y, y[0]]

# fit splines to x=f(u) and y=g(u), treating both as periodic. also note that s=0
# is needed in order to force the spline fit to pass through all the input points.
tck, u = interpolate.splprep([x, y], s=0, per=True)

# evaluate the spline fits for 1000 evenly spaced distance values
xi, yi = interpolate.splev(np.linspace(0, 1, 1000), tck)

# plot the result
fig, ax = plt.subplots(1, 1)
ax.plot(x, y, 'or')
ax.plot(xi, yi, '-b')'''

非常感谢您的帮助。

【问题讨论】：

标签： python scipy curve-fitting bezier spline

【解决方案1】：

您将第一个 x 和 y 值附加到 x 和 y 数组的末尾：

# append the starting x,y coordinates
x = np.r_[x, x[0]]
y = np.r_[y, y[0]]

..这意味着您希望样条曲线在它开始的同一位置结束，然后您告诉interpolate.splprep 函数您需要带有per=True 关键字参数的周期性曲线：

tck, u = interpolate.splprep([x, y], per=True, s=0)

..这会给你你得到的东西..：

只需删除将最后一个 x 和 y 值附加到 x 和 y 数组的两行，并删除 per=True 关键字参数，您就会得到所需的内容：

import numpy as np
from scipy import interpolate
from matplotlib import pyplot as plt

x = np.array([23, 24, 24, 25, 25])
y = np.array([13, 12, 13, 12, 13])

# append the starting x,y coordinates
# x = np.r_[x, x[0]]
# y = np.r_[y, y[0]]

# fit splines to x=f(u) and y=g(u), treating both as periodic. also note that s=0
# is needed in order to force the spline fit to pass through all the input points.
# tck, u = interpolate.splprep([x, y], per=True, s=0)
tck, u = interpolate.splprep([x, y], s=0)

# evaluate the spline fits for 1000 evenly spaced distance values
xi, yi = interpolate.splev(np.linspace(0, 1, 1000), tck)

# plot the result
fig, ax = plt.subplots(1, 1)
ax.plot(x, y, 'or')
ax.plot(xi, yi, '-b')
plt.show()

【讨论】：