python自动重采样数据

概述假设我有以下数据(测量值)：如您所见,有很多尖点(即坡度变化很大的地方).因此,最好在这些点周围再进行一些测量.为此,我编写了一个脚本：>我计算了三个连续点的曲率：Menger曲率：https://en.wikipedia.org/wiki/Menger_curvature#Definition>然后,根据曲率决定应重新采样哪些值....然后迭代

假设我有以下数据(测量值)：

如您所见,有很多尖点(即坡度变化很大的地方).因此,最好在这些点周围再进行一些测量.为此,我编写了一个脚本：

>我计算了三个连续点的曲率：
Menger曲率：https://en.wikipedia.org/wiki/Menger_curvature#Definition
>然后,根据曲率决定应重新采样哪些值.

…然后迭代直到平均曲率下降…但是它不起作用,因为它上升了.你知道为什么吗 ？

这是完整的代码(在x值的长度达到60后停止它)：

import numpy as npimport matplotlib.pyplot as pltdef curvature(A,B,C):    """Calculates the Menger curvature fro three Points,given as numpy arrays.    Sources:    Menger curvature: https://en.wikipedia.org/wiki/Menger_curvature#DeFinition    Area of a triangle given 3 points: https://math.stackexchange.com/questions/516219/finding-out-the-area-of-a-triangle-if-the-coordinates-of-the-three-vertices-are    """    # Pre-check: Making sure that the input points are all numpy arrays    if any(x is not np.ndarray for x in [type(A),type(B),type(C)]):        print("The input points need to be a numpy array,currently it is a ",type(A))    # Augment Columns    A_aug = np.append(A,1)    B_aug = np.append(B,1)    C_aug = np.append(C,1)    # Caclulate Area of Triangle    matrix = np.column_stack((A_aug,B_aug,C_aug))    area = 1/2*np.linalg.det(matrix)    # Special case: Two or more points are equal     if np.all(A == B) or  np.all(B == C):        curvature = 0    else:        curvature = 4*area/(np.linalg.norm(A-B)*np.linalg.norm(B-C)*np.linalg.norm(C-A))    # Return Menger curvature    return curvaturedef values_to_calulate(x,curvature_List,max_curvature):    """Calculates the new x values which need to be calculated    MIDdle point between the three points that were used to calculate the curvature """    i = 0    new_x = np.empty(0)    for curvature in curvature_List:        if curvature > max_curvature:            new_x = np.append(new_x,x[i]+(x[i+2]-x[i])/3 )        i = i+1    return new_xdef plot(x,y,Title,xLabel,yLabel):    """Just to visualize"""    # Plot    plt.scatter(x,y)    plt.plot(x,'-o')    # Give a Title for the sine wave plot    plt.Title(Title)    # Give x axis label for the sine wave plot    plt.xlabel(xLabel)    # Give y axis label for the sine wave plot    plt.ylabel(yLabel)    plt.grID(True,which='both')    plt.axhline(y=0,color='k')    # display the sine wave    plt.show    plt.pause(0.05)### STARTS HERE# Get x values of the sine wavex = np.arange(0,10,1);# Amplitude of the sine wave is sine of a variable like timedef function(x):    return 1+np.sin(x)*np.cos(x)**2y = function(x)# Plot itplot(x,Title='Data',xLabel='Time',yLabel='Amplitude')continue_Loop = Truewhile continue_Loop == True :    curvature_List = np.empty(0)    for i in range(len(x)-2):        # Get the three points        A = np.array([x[i],y[i]])        B = np.array([x[i+1],y[i+1]])        C = np.array([x[i+2],y[i+2]])        # Calculate the curvature        curvature_value = abs(curvature(A,C))        curvature_List = np.append(curvature_List,curvature_value)    print("len: ",len(x) )    print("average curvature: ",np.average(curvature_List))    # Calculate the points that need to be added     x_new = values_to_calulate(x,max_curvature=0.3)    # Add those values to the current x List:    x = np.sort(np.append(x,x_new))    # StopED IT AFTER len(x) == 60    if len(x) >= 60:        continue_Loop = False    # Amplitude of the sine wave is sine of a variable like time    y = function(x)    # Plot it    plot(x,yLabel='Amplitude')@H_419_19@

它应该是这样的：

编辑：

如果让它继续运行…：

最佳答案因此,总结以上我的评论：

>您正在计算曲线的平均曲率,没有理由将其设为0.在每个点上,无论您的点有多近,圆半径都会收敛到该点处的曲率,而不是0.
>一种替代方法是使用两点之间的绝对导数变化：保持采样直到abs(d(df / dx))<. some_threshold其中d(df / dx)=(df / dx)[n]-(df / dx)[n-1] 总结

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