python - 找到xy坐标的边界点

Question

我有一个包含 xy 坐标的文本文件，名为 xy.txt。

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我使用阅读文件

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

我可以用

绘制点

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

数据看起来如下:

我想检索构成形状边界的点的 xy 坐标。类似问题的答案建议使用 Concave Hull。在这个 blog 的帮助下，我编写了以下代码:

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()

输出看起来像

很明显，红点不是边界点。有些被其他点包围，它们都与原始点不同。如何根据原始点定义边界点？请指教

Answer 1

当我尝试重现您的代码时，convexHull 函数完美运行。我更改了您的代码，使黑色和红色圆圈的位置以相同的方式四舍五入。我还减小了红色圆圈的半径，以便您可以更好地查看一切是否合适。

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()

结果:

更新:如果你也需要边界的凹陷部分，你可以使用python包alphashape相反，计算 alpha shape .您的测试数据中的点非常接近，因此我不得不对坐标进行归一化并调整 alpha 值以获得合理的结果。

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()

结果: