查找 xy 坐标的边界点

Question

I have a text file with xy-coordinates called xy.txt .

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I read the file using

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

and I can plot the points with

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

Visually the data looks as follows:

I want to retrieve the xy-coordinates of the points that form the boundary of the shape. Answers on similar questions suggest to use Concave Hull. With the help of this blog I write the following code:

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()

The output looks like

Clearly the red points are not the boundary points. Some are enclosed by other points and they all are different from the original points. How do I define the boundary points in terms of the original points? Please advice

Answer 1

When I try to reproduce your code the convexHull function works perfectly. I changed your code so that the positions of black and red circles are rounded in the same way. And I reduced the radius of the red circles so you can better see if everything fits.

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()

Result:

Update: If you need the concave parts of the boundary, too, you can use the python package alphashape instead and calculate the alpha shape . The points in your test data are very close, so I had to normalize the coordinates and adjust the alpha value to get reasonable results.

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()

Result:

Answer 2

For some contours, the answer of @Markus resulted in the following error:

WARNING:root:Singular matrix. Likely caused by all points lying in an N-1 space.

As a result, I tried a different solution

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)