Gabriel Gabriel - 5 months ago 110
Python Question

Get point associated with Voronoi region (scipy.spatial.Voronoi)

I'm generating a simple 2D Voronoi tessellation, using the scipy.spatial.Voronoi function. I use a random 2D distribution of points (see MWE below).

I need a way to go through each defined region (defined by

scipy.spatial.Voronoi
) and get the coordinates of the point associated to it (ie: the point that said region encloses).

The issue is that there are
N+1
regions (polygons) defined for the
N
points, and I'm not sure what this means.

Here's a MWE that will fail when it gets to the last region:

from scipy.spatial import Voronoi
import numpy as np

# Generate random data.
N = 10
x = [np.random.random() for i in xrange(N)]
y = [np.random.random() for i in xrange(N)]
points = zip(x, y)

# Obtain Voronoi regions.
vor = Voronoi(points)

# Loop through each defined region/polygon
for i, reg in enumerate(vor.regions):

print 'Region:', i
print 'Indices of vertices of Voronoi region:', reg
print 'Associated point:', points[i], '\n'


Another thing I don't understand is why are there empty
vor.regions
stored? According to the docs:


regions: Indices of the Voronoi vertices forming each Voronoi region. -1 indicates vertex outside the Voronoi diagram.


What does an empty region mean?




Add

I tried the
point_region
attribute but apparently I don't understand how it works. It returns indexes outside of the range of the
points
list. For example: in the MWE above it will always show an index
10
for a list of 10 points, which is clearly out of range.

Answer

My bad, I was misreading the docs. It says:

point_region: Index of the Voronoi region for each input point.

and I was using point_region it as if it were the: "Index of the input point for each Voronoi region".

Instead of using:

points[i]

the correct point coordinates for each region can be obtained with:

np.where(vor.point_region == i)[0][0]
Comments