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 np
import matplotlib.pyplot as plt
def 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 curvature
def 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_x
def 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 wave
x = np.arange(0,10,1);
# Amplitude of the sine wave is sine of a variable like time
def function(x):
    return 1+np.sin(x)*np.cos(x)**2
y = function(x)
# Plot it
plot(x,title='Data',xLabel='Time',yLabel='Amplitude')
continue_Loop = True
while 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')

它应该是这样的：

编辑：

如果让它继续运行…：