查找 xy 坐標的邊界點

Question

我有一個名為xy.txt的帶有 xy 坐標的文本文件。

 29.66150677 -98.39336541 29.66150677 -98.39337576 29.66150651 -98.39336541 29.66150328 -98.39337576 29.66150677 -98.39336475 29.66150677 -98.39338611 29.66150393 -98.39338611 29.66150677 -98.39339646 29.66150659 -98.39339646 29.66150677 -98.39339693 29.66151576 -98.39334472 29.66151576 -98.39335506 29.66151511 -98.39334472 29.66151058 -98.39335506 29.66151576 -98.39334322 29.66151576 -98.39336541 29.66151576 -98.39337576 29.66151576 -98.39338611 29.66151576 -98.39339646 29.66151576 -98.39340681 29.66151067 -98.39340681 29.66151576 -98.39341515 29.66152475 -98.39332402 29.66152475 -98.39333437 29.66152443 -98.39332402 29.66151973 -98.39333437 29.66152475 -98.39332332 29.66152475 -98.39334472 29.66152475 -98.39335506 29.66152475 -98.39336541 29.66152475 -98.39337576 29.66152475 -98.39338611 29.66152475 -98.39339646 29.66152475 -98.39340681 29.66152475 -98.39341716 29.66151699 -98.39341716 29.66152475 -98.39342722 29.66153375 -98.39331367 29.66153375 -98.39332402 29.6615302 -98.39331367 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29.66156972 -98.39337576 29.66156972 -98.39338611 29.66156972 -98.39339646 29.66156972 -98.39340681 29.66156972 -98.39341716 29.66156972 -98.39342751 29.66156972 -98.39343786 29.66156972 -98.393442 29.66157871 -98.39327227 29.66157871 -98.39328262 29.66157871 -98.39326327 29.66157871 -98.39329297 29.66157871 -98.39330332 29.66157871 -98.39331367 29.66157871 -98.39332402 29.66157871 -98.39333437 29.66157871 -98.39334472 29.66157871 -98.39335506 29.66157871 -98.39336541 29.66157871 -98.39337576 29.66157871 -98.39338611 29.66157871 -98.39339646 29.66157871 -98.39340681 29.66157871 -98.39341716 29.66157871 -98.39342751 29.66157871 -98.39343786 29.66157871 -98.39344084 29.66158771 -98.39326192 29.66158771 -98.39327227 29.66158097 -98.39326192 29.66158771 -98.39325788 29.66158771 -98.39328262 29.66158771 -98.39329297 29.66158771 -98.39330332 29.66158771 -98.39331367 29.66158771 -98.39332402 29.66158771 -98.39333437 29.66158771 -98.39334472 29.66158771 -98.39335506 29.66158771 -98.39336541 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-98.39335506 29.66160569 -98.39336541 29.66160569 -98.39337576 29.66160569 -98.39338611 29.66160569 -98.39339646 29.66160569 -98.39340681 29.66160569 -98.39341716 29.66160569 -98.39342751 29.66160569 -98.39343291 29.66161468 -98.39325157 29.66161468 -98.39326192 29.66161468 -98.39324921 29.66161468 -98.39327227 29.66161468 -98.39328262 29.66161468 -98.39329297 29.66161468 -98.39330332 29.66161468 -98.39331367 29.66161468 -98.39332402 29.66161468 -98.39333437 29.66161468 -98.39334472 29.66161468 -98.39335506 29.66161468 -98.39336541 29.66161468 -98.39337576 29.66161468 -98.39338611 29.66161468 -98.39339646 29.66161468 -98.39340681 29.66161468 -98.39341716 29.66161468 -98.39342751 29.66161468 -98.39342823 29.66161592 -98.39342751 29.66162368 -98.39325157 29.66162368 -98.39326192 29.66162368 -98.39324697 29.66162368 -98.39327227 29.66162368 -98.39328262 29.66162368 -98.39329297 29.66162368 -98.39330332 29.66162368 -98.39331367 29.66162368 -98.39332402 29.66162368 -98.39333437 29.66162368 -98.39334472 29.66162368 -98.39335506 29.66162368 -98.39336541 29.66162368 -98.39337576 29.66162368 -98.39338611 29.66162368 -98.39339646 29.66162368 -98.39340681 29.66162368 -98.39341716 29.66162368 -98.39342302 29.66163267 -98.39325157 29.66163267 -98.39326192 29.66163267 -98.39324642 29.66163267 -98.39327227 29.66163267 -98.39328262 29.66163267 -98.39329297 29.66163267 -98.39330332 29.66163267 -98.39331367 29.66163267 -98.39332402 29.66163267 -98.39333437 29.66163267 -98.39334472 29.66163267 -98.39335506 29.66163267 -98.39336541 29.66163267 -98.39337576 29.66163267 -98.39338611 29.66163267 -98.39339646 29.66163267 -98.39340681 29.66163267 -98.39341716 29.66163267 -98.39341722 29.66163275 -98.39341716 29.66164166 -98.39325157 29.66164166 -98.39326192 29.66164166 -98.39324588 29.66164166 -98.39327227 29.66164166 -98.39328262 29.66164166 -98.39329297 29.66164166 -98.39330332 29.66164166 -98.39331367 29.66164166 -98.39332402 29.66164166 -98.39333437 29.66164166 -98.39334472 29.66164166 -98.39335506 29.66164166 -98.39336541 29.66164166 -98.39337576 29.66164166 -98.39338611 29.66164166 -98.39339646 29.66164166 -98.39340681 29.66164166 -98.39341103 29.66164749 -98.39340681 29.66165066 -98.39325157 29.66165066 -98.39326192 29.66165066 -98.39324533 29.66165066 -98.39327227 29.66165066 -98.39328262 29.66165066 -98.39329297 29.66165066 -98.39330332 29.66165066 -98.39331367 29.66165066 -98.39332402 29.66165066 -98.39333437 29.66165066 -98.39334472 29.66165066 -98.39335506 29.66165066 -98.39336541 29.66165066 -98.39337576 29.66165066 -98.39338611 29.66165066 -98.39339646 29.66165066 -98.39340447 29.66165965 -98.39325157 29.66165965 -98.39326192 29.66165965 -98.39324479 29.66165965 -98.39327227 29.66165965 -98.39328262 29.66165965 -98.39329297 29.66165965 -98.39330332 29.66165965 -98.39331367 29.66165965 -98.39332402 29.66165965 -98.39333437 29.66165965 -98.39334472 29.66165965 -98.39335506 29.66165965 -98.39336541 29.66165965 -98.39337576 29.66165965 -98.39338611 29.66165965 -98.39339646 29.66165965 -98.39339783 29.6616615 -98.39339646 29.66166864 -98.39325157 29.66166864 -98.39326192 29.66166864 -98.39324424 29.66166864 -98.39327227 29.66166864 -98.39328262 29.66166864 -98.39329297 29.66166864 -98.39330332 29.66166864 -98.39331367 29.66166864 -98.39332402 29.66166864 -98.39333437 29.66166864 -98.39334472 29.66166864 -98.39335506 29.66166864 -98.39336541 29.66166864 -98.39337576 29.66166864 -98.39338611 29.66166864 -98.39339119 29.66167552 -98.39338611 29.66167764 -98.39325157 29.66167764 -98.39326192 29.66167764 -98.3932437 29.66167764 -98.39327227 29.66167764 -98.39328262 29.66167764 -98.39329297 29.66167764 -98.39330332 29.66167764 -98.39331367 29.66167764 -98.39332402 29.66167764 -98.39333437 29.66167764 -98.39334472 29.66167764 -98.39335506 29.66167764 -98.39336541 29.66167764 -98.39337576 29.66167764 -98.39338455 29.66168663 -98.39325157 29.66168663 -98.39326192 29.66168663 -98.39324315 29.66168663 -98.39327227 29.66168663 -98.39328262 29.66168663 -98.39329297 29.66168663 -98.39330332 29.66168663 -98.39331367 29.66168663 -98.39332402 29.66168663 -98.39333437 29.66168663 -98.39334472 29.66168663 -98.39335506 29.66168663 -98.39336541 29.66168663 -98.39337576 29.66168663 -98.39337791 29.66168954 -98.39337576 29.66169562 -98.39325157 29.66169562 -98.39326192 29.66169562 -98.39324277 29.66169562 -98.39327227 29.66169562 -98.39328262 29.66169562 -98.39329297 29.66169562 -98.39330332 29.66169562 -98.39331367 29.66169562 -98.39332402 29.66169562 -98.39333437 29.66169562 -98.39334472 29.66169562 -98.39335506 29.66169562 -98.39336541 29.66169562 -98.39337127 29.66170356 -98.39336541 29.66170462 -98.39325157 29.66170462 -98.39326192 29.66170462 -98.39324245 29.66170462 -98.39327227 29.66170462 -98.39328262 29.66170462 -98.39329297 29.66170462 -98.39330332 29.66170462 -98.39331367 29.66170462 -98.39332402 29.66170462 -98.39333437 29.66170462 -98.39334472 29.66170462 -98.39335506 29.66170462 -98.39336463 29.66171361 -98.39325157 29.66171361 -98.39326192 29.66171361 -98.39324213 29.66171361 -98.39327227 29.66171361 -98.39328262 29.66171361 -98.39329297 29.66171361 -98.39330332 29.66171361 -98.39331367 29.66171361 -98.39332402 29.66171361 -98.39333437 29.66171361 -98.39334472 29.66171361 -98.39335506 29.66171361 -98.39335799 29.66171758 -98.39335506 29.6617226 -98.39325157 29.6617226 -98.39326192 29.6617226 -98.393242 29.6617226 -98.39327227 29.6617226 -98.39328262 29.6617226 -98.39329297 29.6617226 -98.39330332 29.6617226 -98.39331367 29.6617226 -98.39332402 29.6617226 -98.39333437 29.6617226 -98.39334472 29.6617226 -98.39335135 29.66173159 -98.39334472 29.6617316 -98.39325157 29.6617316 -98.39326192 29.6617316 -98.393242 29.6617316 -98.39327227 29.6617316 -98.39328262 29.6617316 -98.39329297 29.6617316 -98.39330332 29.6617316 -98.39331367 29.6617316 -98.39332402 29.6617316 -98.39333437 29.6617316 -98.39334471 29.66174059 -98.39325157 29.66174059 -98.39326192 29.66174059 -98.393242 29.66174059 -98.39327227 29.66174059 -98.39328262 29.66174059 -98.39329297 29.66174059 -98.39330332 29.66174059 -98.39331367 29.66174059 -98.39332402 29.66174059 -98.39333437 29.66174059 -98.39333807 29.66174561 -98.39333437 29.66174958 -98.39325157 29.66174958 -98.39326192 29.66174958 -98.39324293 29.66174958 -98.39327227 29.66174958 -98.39328262 29.66174958 -98.39329297 29.66174958 -98.39330332 29.66174958 -98.39331367 29.66174958 -98.39332402 29.66174958 -98.39333143 29.66175858 -98.39325157 29.66175858 -98.39326192 29.66176663 -98.39325157 29.66176757 -98.39326192 29.66175858 -98.39324585 29.66175858 -98.39327227 29.66175858 -98.39328262 29.66175858 -98.39329297 29.66175858 -98.39330332 29.66175858 -98.39331367 29.66175858 -98.39332402 29.66175858 -98.39332427 29.6617589 -98.39332402 29.66176757 -98.39327227 29.66177412 -98.39326192 29.66177656 -98.39327227 29.66176757 -98.3932525 29.66176757 -98.39328262 29.66176757 -98.39329297 29.66176757 -98.39330332 29.66176757 -98.39331367 29.66177543 -98.39330332 29.66176974 -98.39331367 29.66176757 -98.3933162 29.66177656 -98.39328262 29.66177775 -98.39327227 29.66177872 -98.39328262 29.66177656 -98.39326599 29.66177656 -98.39329297 29.66177855 -98.39329297 29.66177656 -98.39330028

我使用讀取文件

import numpy as np
xy =  np.loadtxt('xy.txt')
x, y = xy[:, 0], xy[:, 1]

我可以 plot 點與

import matplotlib.pyplot as plt
plt.plot(x, y, 'o', color='black', markersize=6)
plt.show()

從視覺上看，數據如下所示：

我想檢索形成形狀邊界的點的 xy 坐標。 類似問題的答案建議使用凹殼。 在此博客的幫助下，我編寫了以下代碼：

from scipy import spatial
hull = spatial.ConvexHull(xy, incremental=False, qhull_options='Qt')
hull_indices = hull.vertices

boundary_x = []
boundary_y = []

for i in range(len(hull_indices)):
    index = hull_indices[i]
    boundary_x.append(xy[index, 0].astype('float32'))
    boundary_y.append(xy[index, 1].astype('float32'))

plt.plot(boundary_x, boundary_y, 'o', color='red', markersize=6)
plt.show()

output 看起來像

顯然紅點不是邊界點。 有些被其他點包圍，它們都與原始點不同。 如何根據原始點定義邊界點？ 請指教

Answer 1

當我嘗試重現您的代碼時，convexHull 函數可以完美運行。 我更改了您的代碼，以便黑色和紅色圓圈的位置以相同的方式四舍五入。 我減小了紅色圓圈的半徑，這樣你就可以更好地查看一切是否合適。

import numpy as np
import matplotlib.pyplot as plt
from scipy import spatial


xy = np.loadtxt('xy.txt')
x, y = xy[:, 0].astype('float64'), xy[:, 1].astype('float64')

hull = spatial.ConvexHull(xy, incremental=False, qhull_options='Qt')
hull_indices = hull.vertices

boundary_x = []
boundary_y = []

for i in range(len(hull_indices)):
    index = hull_indices[i]
    boundary_x.append(xy[index, 0].astype('float64'))
    boundary_y.append(xy[index, 1].astype('float64'))

plt.plot(x, y, 'o', color='black', markersize=6)
plt.plot(boundary_x, boundary_y, 'o', color='red', markersize=4)

plt.show()

結果：

更新：如果您也需要邊界的凹入部分，您可以改用 python 包alphashape並計算alpha shape 。 您的測試數據中的點非常接近，因此我必須對坐標進行歸一化並調整 alpha 值以獲得合理的結果。

import numpy as np
import matplotlib.pyplot as plt
import alphashape


data = np.loadtxt('xy.txt')
xy = (data + [-29.0, 98.0]) * 10
x, y = xy[:, 0], xy[:, 1]
shape = alphashape.alphashape(xy, alpha=500.0)
shape_x, shape_y = shape.exterior.coords.xy

plt.plot(x, y, 'o', color='black', markersize=6)
plt.plot(shape_x, shape_y, 'o', color='red', markersize=4)

plt.show()

結果：

Answer 2

對於某些輪廓，@Markus 的答案導致以下錯誤：

警告：根：奇異矩陣。 可能是由位於 N-1 空間中的所有點引起的。

結果，我嘗試了不同的解決方案

import numpy as np
from shapely.geometry import Polygon


def get_boundary(path: str) -> list:
    coordinates = np.loadtxt(path)
    x, y = coordinates[:, 0], coordinates[:, 1]
    green = Polygon(list(zip(x, y)))

    # get boundary
    boundary_x, boundary_y = green.exterior.xy
    return list(zip(boundary_x, boundary_y))

get_boundary(path=PATH)