无法在 Python 中绘制曲率的准确切线

Question

我有一个曲率数据集，我需要找到曲线的切线，但不幸的是，这离曲线有点远。请指导我与问题相关的问题解决方案。谢谢！我的代码如下：

fig, ax1 = plt.subplots()
chData_m = efficient.get('Car.Road.y')  

x_fit = chData_m.timestamps
y_fit = chData_m.samples

fittedParameters = np.polyfit(x_fit[:],y_fit[:],1)

f = plt.figure(figsize=(800/100.0, 600/100.0), dpi=100)
axes = f.add_subplot(111)

    # first the raw data as a scatter plot
axes.plot(x_fit, y_fit,  'D')

    # create data for the fitted equation plot
xModel = np.linspace(min(x_fit), max(x_fit))
yModel = np.polyval(fittedParameters, xModel)

    # now the model as a line plot
axes.plot(xModel, yModel)

axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label

    # polynomial derivative from numpy
deriv = np.polyder(fittedParameters)

    # for plotting
minX = min(x_fit)
maxX = max(x_fit)

    # value of derivative (slope) at a specific X value, so
    # that a straight line tangent can be plotted at the point
    # you might place this code in a loop to animate
pointVal = 10.0 # example X value
y_value_at_point = np.polyval(fittedParameters, pointVal)
slope_at_point = np.polyval(deriv, pointVal)

ylow = (minX - pointVal) * slope_at_point + y_value_at_point
yhigh = (maxX - pointVal) * slope_at_point + y_value_at_point

    # now the tangent as a line plot
axes.plot([minX, maxX], [ylow, yhigh])

plt.show()
plt.close('all') # clean up after using pyplot

输出为：

Answer 1

我不确定您想如何使用 numpy polyfit/polyval 来确定正切公式。我在这里描述了一种不同的方法。这种方法的优点是它对函数的性质没有任何假设。缺点是对垂直切线不起作用
为了安全起见，我考虑了这两种情况，即评估的 x 值是您系列中的数据点，而事实并非如此。可能会出现一些问题，因为我看到您在问题中提到了时间戳，但没有通过提供玩具数据集来指定它们的性质 - 因此，此版本可能会或可能不会使用原始数据的日期时间对象或时间戳：

import matplotlib.pyplot as plt
import numpy as np

#generate fake data with unique random x-values between 0 and 70
def func(x, a=0, b=100, c=1, n=3.5):
    return a + (b/(1+(c/x)**n))
np.random.seed(123)
x = np.random.choice(range(700000), 100)/10000
x.sort()
y = func(x, 1, 2, 15, 2.4)


#data point to evaluate
xVal = 29

#plot original data
fig, ax = plt.subplots()
ax.plot(x, y, c="blue", label="data")

#calculate gradient
slope = np.gradient(y, x)

#determine slope and intercept at xVal
ind1 = (np.abs(x - xVal)).argmin()
#case 1 the value is a data point
if xVal == x[ind1]:
    yVal, slopeVal = y[ind1], slope[ind1]    
#case 2 the value lies between to data points
#in which case we approximate linearly from the two nearest data points
else:
    if xVal < x[ind1]:
        ind1, ind2 = ind1-1, ind1
    else:
        ind1, ind2 = ind1, ind1+1         
    yVal = y[ind1] + (y[ind2]-y[ind1]) * (xVal-x[ind1]) / (x[ind2]-x[ind1])
    slopeVal = slope[ind1] + (slope[ind2]-slope[ind1]) * (xVal-x[ind1]) / (x[ind2]-x[ind1])
intercVal = yVal - slopeVal * xVal    

ax.plot([x.min(), x.max()], [slopeVal*x.min()+intercVal, slopeVal*x.max()+intercVal], color="green", 
        label=f"tangent\nat point [{xVal:.1f}, {yVal:.1f}]\nwith slope {slopeVal:.2f}\nand intercept {intercVal:.2f}" )
ax.set_ylim(0.8 * y.min(), 1.2 * y.max())
ax.legend()

plt.show()

无法在 Python 中绘制曲率的准确切线

Unable to plot an accurate tangent to a curvature in Python

python

curve

numpy

matplotlib