Issue
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
Solution
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:
Answered By - Markus
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