python之如何在 Python 中插入二维曲线_编程设计

我有一组 x 和 y 坐标，它是一条曲线/形状，我想要使曲线平滑/锐利并绘制图形。

我尝试了不同的插值来平滑曲线/形状，但它仍然不符合我的期望。使用点绘制平滑的曲线/形状。

像下面这样，用x,y点得到一个平滑的圆/曲线

但是，我得到了类似的东西

圆.jpg

曲线.jpg

正方形.jpg

我在样条插值和 rbf 插值方面也遇到了麻烦。

对于 cubic_spline_interpolation，我得到了

ValueError: Error on input data

对于 univariate_spline_interpolated，我得到了

ValueError: x must be strictly increasing

对于rbf，我得到了

numpy.linalg.linalg.LinAlgError: Matrix is singular.

我想修复它们并获得正确的锐度和曲线。非常感谢您的帮助。

编辑对于无法下载源代码和x,y坐标文件的，我贴出有问题的代码和x,y坐标。

以下是我的代码:

#!/usr/bin/env python3 
from std_lib import * 
 
import os 
import numpy as np 
import cv2 
 
from scipy import interpolate 
import matplotlib.pyplot as plt 
 
CUR_DIR = os.getcwd() 
CIRCLE_FILE = "circle.txt" 
CURVE_FILE  = "curve.txt" 
SQUARE_FILE = "square.txt" 
 
#test 
CIRCLE_NAME = "circle" 
CURVE_NAME  = "curve" 
SQUARE_NAME = "square" 
 
SYS_TOKEN_CNT = 2   # x, y 
 
total_pt_cnt = 0        # total no. of points       
x_arr = np.array([])    # x position set 
y_arr = np.array([])    # y position set 
 
def convert_coord_to_array(file_path): 
    global total_pt_cnt 
    global x_arr 
    global y_arr 
 
    if file_path == "": 
        return FALSE 
 
    with open(file_path) as f: 
        content = f.readlines() 
 
    content = [x.strip() for x in content]  
 
    total_pt_cnt = len(content) 
 
    if (total_pt_cnt <= 0): 
        return FALSE 
 
    ## 
    x_arr = np.empty((0, total_pt_cnt)) 
    y_arr = np.empty((0, total_pt_cnt)) 
 
    #compare the first and last x  
    # if ((content[0][0]) > (content[-1])): 
        # is_reverse = TRUE 
 
    for x in content: 
        token_cnt = get_token_cnt(x, ',')  
 
        if (token_cnt != SYS_TOKEN_CNT): 
            return FALSE 
 
        for idx in range(token_cnt): 
            token_string = get_token_string(x, ',', idx) 
            token_string = token_string.strip() 
            if (not token_string.isdigit()):  
                return FALSE 
 
            # save x, y set 
            if (idx == 0): 
                x_arr = np.append(x_arr, int(token_string)) 
            else: 
                y_arr = np.append(y_arr, int(token_string)) 
 
    return TRUE 
 
def linear_interpolation(fig, axs): 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    f = interpolate.interp1d(xnew , y_arr) 
 
    axs.plot(xnew, f(xnew)) 
    axs.set_title('linear') 
 
def cubic_interpolation(fig, axs): 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    f = interpolate.interp1d(xnew , y_arr, kind='cubic') 
 
    axs.plot(xnew, f(xnew)) 
    axs.set_title('cubic') 
 
def cubic_spline_interpolation(fig, axs): 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    tck = interpolate.splrep(x_arr, y_arr, s=0) #always fail (ValueError: Error on input data) 
    ynew = interpolate.splev(xnew, tck, der=0) 
 
    axs.plot(xnew, ynew) 
    axs.set_title('cubic spline') 
 
def parametric_spline_interpolation(fig, axs): 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    tck, u = interpolate.splprep([x_arr, y_arr], s=0) 
    out = interpolate.splev(xnew, tck) 
 
    axs.plot(out[0], out[1]) 
    axs.set_title('parametric spline') 
 
def univariate_spline_interpolated(fig, axs):    
    s = interpolate.InterpolatedUnivariateSpline(x_arr, y_arr)# ValueError: x must be strictly increasing 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    ynew = s(xnew) 
 
    axs.plot(xnew, ynew) 
    axs.set_title('univariate spline') 
 
def rbf(fig, axs): 
    xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr)) 
    rbf = interpolate.Rbf(x_arr, y_arr) # numpy.linalg.linalg.LinAlgError: Matrix is singular. 
    fi = rbf(xnew) 
 
    axs.plot(xnew, fi) 
    axs.set_title('rbf') 
 
def interpolation(): 
    fig, axs = plt.subplots(nrows=4) 
    axs[0].plot(x_arr, y_arr, 'r-') 
    axs[0].set_title('org') 
 
    cubic_interpolation(fig, axs[1]) 
    # cubic_spline_interpolation(fig, axs[2])  
    parametric_spline_interpolation(fig, axs[2]) 
    # univariate_spline_interpolated(fig, axs[3]) 
    # rbf(fig, axs[3])         
    linear_interpolation(fig, axs[3]) 
 
    plt.show() 
 
#------- main ------- 
if __name__ == "__main__": 
    # np.seterr(divide='ignore', invalid='ignore') 
 
    file_name = CUR_DIR + "/" + CIRCLE_FILE  
    convert_coord_to_array(file_name)   
    #file_name = CUR_DIR + "/" + CURVE_FILE  
    #convert_coord_to_array(file_name)  
    #file_name = CUR_DIR + "/" + SQUARE_FILE  
    #convert_coord_to_array(file_name)  
    # 
    interpolation()

圆x，y坐标

已解决

def linear_interpolateion(self, x, y): 
 
        points = np.array([x, y]).T  # a (nbre_points x nbre_dim) array 
 
        # Linear length along the line: 
        distance = np.cumsum( np.sqrt(np.sum( np.diff(points, axis=0)**2, axis=1 )) ) 
        distance = np.insert(distance, 0, 0) 
 
        alpha = np.linspace(distance.min(), int(distance.max()), len(x)) 
        interpolator =  interpolate.interp1d(distance, points, kind='slinear', axis=0) 
        interpolated_points = interpolator(alpha) 
 
        out_x = interpolated_points.T[0] 
        out_y = interpolated_points.T[1] 
 
        return out_x, out_y

请您参考如下方法:

因为一般二维曲线需要插值，即 (x, y)=f(s) 其中 s 是坐标曲线，而不是 y = f(x)，必须首先计算沿线 s 的距离。然后，相对于s对每个坐标进行插值。 (例如，在圆的情况下 y = f(x) 有两个解决方案)

s(或此处代码中的 distance)计算为给定点之间每个线段长度的累积和。

import numpy as np 
from scipy.interpolate import interp1d 
import matplotlib.pyplot as plt 
 
# Define some points: 
points = np.array([[0, 1, 8, 2, 2], 
                   [1, 0, 6, 7, 2]]).T  # a (nbre_points x nbre_dim) array 
 
# Linear length along the line: 
distance = np.cumsum( np.sqrt(np.sum( np.diff(points, axis=0)**2, axis=1 )) ) 
distance = np.insert(distance, 0, 0)/distance[-1] 
 
# Interpolation for different methods: 
interpolations_methods = ['slinear', 'quadratic', 'cubic'] 
alpha = np.linspace(0, 1, 75) 
 
interpolated_points = {} 
for method in interpolations_methods: 
    interpolator =  interp1d(distance, points, kind=method, axis=0) 
    interpolated_points[method] = interpolator(alpha) 
 
# Graph: 
plt.figure(figsize=(7,7)) 
for method_name, curve in interpolated_points.items(): 
    plt.plot(*curve.T, '-', label=method_name); 
 
plt.plot(*points.T, 'ok', label='original points'); 
plt.axis('equal'); plt.legend(); plt.xlabel('x'); plt.ylabel('y');

给出:

关于图表，您似乎正在寻找一种平滑方法而不是点的插值。这里是一种类似的方法，用于在给定曲线的每个坐标上分别拟合样条(请参阅 Scipy UnivariateSpline):

import numpy as np 
import matplotlib.pyplot as plt 
 
from scipy.interpolate import UnivariateSpline 
 
# Define some points: 
theta = np.linspace(-3, 2, 40) 
points = np.vstack( (np.cos(theta), np.sin(theta)) ).T 
 
# add some noise: 
points = points + 0.05*np.random.randn(*points.shape) 
 
# Linear length along the line: 
distance = np.cumsum( np.sqrt(np.sum( np.diff(points, axis=0)**2, axis=1 )) ) 
distance = np.insert(distance, 0, 0)/distance[-1] 
 
# Build a list of the spline function, one for each dimension: 
splines = [UnivariateSpline(distance, coords, k=3, s=.2) for coords in points.T] 
 
# Computed the spline for the asked distances: 
alpha = np.linspace(0, 1, 75) 
points_fitted = np.vstack( spl(alpha) for spl in splines ).T 
 
# Graph: 
plt.plot(*points.T, 'ok', label='original points'); 
plt.plot(*points_fitted.T, '-r', label='fitted spline k=3, s=.2'); 
plt.axis('equal'); plt.legend(); plt.xlabel('x'); plt.ylabel('y');

给出: