如何在 Python 中插入 2D 曲线 [英] How to interpolate a 2D curve in Python

查看：26 发布时间：2021/12/31 12:25:59 python scipy interpolation

本文介绍了如何在 Python 中插入 2D 曲线的处理方法，对大家解决问题具有一定的参考价值，需要的朋友们下面随着小编来一起学习吧！

问题描述

我有一组 x &y 坐标是曲线/形状，我想要平滑曲线/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，使用x,y点得到平滑的圆/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

<块引用>

ValueError:输入数据错误

对于 univariate_spline_interpolated，我得到 <块引用>

ValueError: x 必须严格递增

对于rbf，我得到了

<块引用>

numpy.linalg.linalg.LinAlgError:矩阵是奇异的.

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.

编辑对于那些不能下载源代码和x,y坐标文件的，我把有问题的代码和x,y坐标贴出来.

以下是我的代码:

#!/usr/bin/env python3从 std_lib 导入 *导入操作系统将 numpy 导入为 np导入 cv2从 scipy 导入插值导入 matplotlib.pyplot 作为 pltCUR_DIR = os.getcwd()CIRCLE_FILE = "circle.txt"CURVE_FILE = "曲线.txt"SQUARE_FILE = "square.txt"#测试CIRCLE_NAME = "圆圈"CURVE_NAME = "曲线"SQUARE_NAME = "正方形"SYS_TOKEN_CNT = 2 # x, ytotal_pt_cnt = 0 # 总数.点数x_arr = np.array([]) # x 位置集y_arr = np.array([]) # y 位置集def convert_coord_to_array(file_path):全局 total_pt_cnt全局 x_arr全局 y_arr如果 file_path == "":返回错误使用 open(file_path) 作为 f:内容 = f.readlines()content = [x.strip() for x in content]total_pt_cnt = len(内容)如果(total_pt_cnt <= 0):返回错误##x_arr = np.empty((0, total_pt_cnt))y_arr = np.empty((0, total_pt_cnt))#比较第一个和最后一个x# if ((content[0][0]) > (content[-1])):# is_reverse = TRUE对于内容中的 x:token_cnt = get_token_cnt(x, ',')如果(token_cnt ！= SYS_TOKEN_CNT):返回错误对于范围内的 idx(token_cnt):token_string = get_token_string(x, ',', idx)token_string = token_string.strip()如果(不是 token_string.isdigit()):返回错误# 保存 x, y 集如果(idx == 0):x_arr = np.append(x_arr, int(token_string))别的:y_arr = np.append(y_arr, int(token_string))返回真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('线性')defcubic_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('立方')defcubine_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) #总是失败(ValueError: Error on input data)ynew = interpolate.splev(xnew, tck, der=0)axs.plot(xnew, ynew)axs.set_title('三次样条')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(出[0]，出[1])axs.set_title('参数样条')def univariate_spline_interpolated(fig, axs):s = interpolate.InterpolatedUnivariateSpline(x_arr, y_arr)# ValueError: x 必须严格递增xnew = np.linspace(x_arr.min(), x_arr.max(), len(x_arr))ynew = s(xnew)axs.plot(xnew, ynew)axs.set_title('单变量样条')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:矩阵是奇异的.fi = rbf(xnew)axs.plot(xnew, fi)axs.set_title('rbf')定义插值():图, axs = plt.subplots(nrows=4)axs[0].plot(x_arr, y_arr, 'r-')axs[0].set_title('org')三次插值(图，轴 [1])#cubic_spline_interpolation(fig, axs[2])参数样条插值(图，轴[2])# univariate_spline_interpolated(fig, axs[3])# rbf(fig, axs[3])线性插值(图，轴 [3])plt.show()# -  -  - - 主要的  -  -  - -如果 __name__ == "__main__":# np.seterr(divide='ignore', invalid='ignore')文件名 = CUR_DIR + "/" + CIRCLE_FILEconvert_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)#插值()

圆 x,y 坐标

307, 91308, 90339, 90340, 91348, 91349, 92351, 92352, 93357, 93358, 94361, 94362, 95364, 95365, 96369, 96370, 97374, 97375, 98376, 98377, 99379, 99380, 100382, 100383, 101386, 101387, 102389, 102390, 103392, 103393, 104394, 104395, 105398, 105399, 106400, 106401, 107402, 107403, 108405, 108406, 109407, 109408, 110410, 110411, 111413、111414, 112415, 112416, 113417, 113418, 114419, 114420, 115421, 115422, 116423, 116425, 118426, 118428, 120429, 120430, 121430, 122431, 122433, 124434, 124435, 125435, 126437, 128437, 129441, 133441, 134442, 135442, 137443, 137444, 138444, 140445, 141445, 142446, 143446, 146447, 147447, 148448, 149448, 153449, 154449, 191448, 192448, 223447, 224447, 240446, 241446, 242445, 243445, 248444, 249444, 253443, 254443, 256442, 257442, 259441, 260441, 263440, 264440, 267439, 268439, 269438, 270438, 272436, 274436, 275435, 276435, 279434, 280434, 281433, 282433, 283431, 285431, 288429, 290429, 291428, 292428、293426, 295426, 296425, 297425, 298424, 299424, 300423、301423、303422、304422、305420、307420, 308419、309419、310417, 312417, 313415, 315415, 316414、317414、318412、320411、320410, 321410, 322409、323409、324408、325407、325402、330401、330401, 331399, 333398, 333395, 336395, 337394, 338393, 338390, 341388, 341387, 342387, 343386, 344384, 344383, 345382, 345380, 347379, 347377, 349376, 349374, 351373, 351373, 352372, 353370, 353369, 354368, 354367, 355366, 355365, 356364, 356363, 357362, 357359, 360358, 360357, 361356, 361355, 362353, 362353, 363352, 364348, 364347, 365314, 365313, 364297, 364296, 363284, 363283, 362280, 362279, 361273, 361272, 360271, 360270, 359265, 359264, 358262, 358261, 357260, 357258, 355257, 355256, 354255, 354252, 351251, 351246, 346245, 346237, 338237, 337235, 335234, 335231, 332231, 331230, 330230, 329222, 321222, 320217, 315217, 314213, 310213、309210, 306210, 305204, 299204, 298203, 297203, 296199, 292199, 291198, 290198, 289197, 289194, 286194, 285191, 282191, 280187, 276187, 275185, 273185, 271184, 270184, 269183, 268183, 266182, 265182, 264180, 262180, 261179, 260179, 258177, 256177, 254176, 253176, 251175, 250175, 249174, 248174, 246173, 245173, 243171, 241171, 237170, 236170, 232169, 231169, 230168, 229168, 211169, 210169, 205170, 204170, 199171, 198171, 195172, 194172, 193173, 192173, 189174, 188174, 185176, 183176, 180177, 179177, 177178, 176178, 175179, 174179, 173180, 172180, 170182, 168182, 167183, 166183, 165185, 163185, 162186, 161186, 160189, 157189, 156191, 154191, 153192, 152192, 149197, 144197, 143203, 137204, 137207, 134208, 134211, 131213, 131216, 128217, 128218, 127219, 127221, 125222, 125223, 124224, 124225, 123226, 123227, 122228, 122229, 121231, 121233, 119234, 119237, 116239, 116240, 115241, 115242, 114244, 114245, 113246, 113247, 112250, 112251, 111252, 111253, 110256, 110257, 109258, 109259, 108262, 108263, 107266, 107267, 106269, 106272, 103274, 103275, 102276, 102277, 101278, 101279, 100281, 100282, 99283, 99284, 98286, 98287, 97288, 97289, 96290, 96291, 95293, 95295, 93298, 93299, 92302, 92303, 91

已解决

def linear_interpolateion(self, x, y):points = np.array([x, y]).T # a (nbre_points x nbre_dim) 数组# 沿线的线性长度:距离 = np.cumsum( np.sqrt(np.sum( np.diff(points, axis=0)**2, axis=1 )) )距离 = np.insert(距离, 0, 0)alpha = np.linspace(distance.min(), int(distance.max()), len(x))插值器 = interpolate.interp1d(距离, 点, kind='slinear', axis=0)interpolated_points = interpolator(alpha)out_x = interpolated_points.T[0]out_y = interpolated_points.T[1]返回 out_x, out_y

解决方案

因为 interpolation 是通用 2d 曲线所需要的，即 (x, y)=f(s) 其中s 是沿曲线的坐标，而不是y = f(x)，必须计算沿线的距离s第一的.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段长度的累积总和.

将 numpy 导入为 np从 scipy.interpolate 导入 interp1d导入 matplotlib.pyplot 作为 plt# 定义一些点:点 = np.array([[0, 1, 8, 2, 2],[1, 0, 6, 7, 2]]).T #一个(nbre_points x nbre_dim)数组# 沿线的线性长度:距离 = np.cumsum( np.sqrt(np.sum( np.diff(points, axis=0)**2, axis=1 )) )距离 = np.insert(distance, 0, 0)/distance[-1]# 不同方法的插值:interpolations_methods = ['slinear', 'quadratic', 'cubic']阿尔法 = np.linspace(0, 1, 75)interpolated_points = {}对于interpolations_methods 中的方法:插值器 = interp1d(距离，点，种类=方法，轴=0)interpolated_points[method] = interpolator(alpha)# 图表:plt.figure(figsize=(7,7))对于 method_name，interpolated_points.items() 中的曲线:plt.plot(*curve.T, '-', label=method_name);plt.plot(*points.T, 'ok', label='原始点');plt.axis('相等');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(参见

I have a set of x & y coordinate which is a curve / shape, I want the smooth the curve / sharp and plot a graph.

I tried different interpolation to smooth the curve / shape, But it still cannot fit my expectation. Using point to draw a smooth curve / shape.

Like the following, using x, y point to get a smooth circle / curve

However, I get something like

circle.jpg

curve.jpg

square.jpg

I also get trouble on spline interpolation, and rbf interpolation.

for cubic_spline_interpolation, I got

ValueError: Error on input data

for univariate_spline_interpolated, I got

ValueError: x must be strictly increasing

for rbf, I got

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

I have on idea to fix them and get correct sharp and curve. Many thanks for help.

Edit For those cannot download the source code and x, y coordinate file, I post the code and x, y coordinate in question.

The following is my code:

#!/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()

circle x, y coordinate

Solved

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

解决方案

Because the interpolation is wanted for generic 2d curve i.e. (x, y)=f(s) where s is the coordinates along the curve, rather than y = f(x), the distance along the line s have to be computed first. Then, the interpolation for each coordinates is performed relatively to s. (for instance, in the circle case y = f(x) have two solutions)

s (or distance in the code here) is calculated as the cumulative sum of the length of each segments between the given points.

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');

which gives:

Regarding the graphs, it seems you are looking for a smoothing method rather than an interpolation of the points. Here, is a similar approach use to fit a spline separately on each coordinates of the given curve (see 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');

which gives:

这篇关于如何在 Python 中插入 2D 曲线的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！

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如何在 Python 中插入 2D 曲线 [英] How to interpolate a 2D curve in Python

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