Voronoi Diagram Edges: How to get edges in the form (point1, point2) from a scipy.spatial.Voronoi object?

Question

I have spent a great deal of time now trying to obtain edges from the scipy.spatial.Voronoi diagram to no avail. Here is the main documentation: http://docs.scipy.org/doc/scipy-dev/reference/generated/scipy.spatial.Voronoi.html

If you create a Voronoi Diagram like so:

points = np.array([[0, 0], [0, 1], [0, 2], [1, 0], [1, 1], [1, 2],
[2, 0], [2, 1], [2, 2]]) //Or feel free to use any set of points

then you have access to the following object properties:

vor.regions
vor.max_bound
vor.ndim
vor.ridge_dict
vor.ridge_points
vor.ridge_vertices
vor.npoints
vor.point_region
vor.points

But is unclear how to combine these to get edges in the form (point1, point2) for 2d voronoi diagrams? I know edges exist because you can plot the voronoi diagram and its edgres and vertices because you can do the following:

voronoi_plot_2d(vor)
plt.show()

which clearly depicts voronoi edgres - how to get a list of them and their starting and endpoints? Its okay if I only get the solid edges (not the dotted ones which go unbounded off the plot)

Prager

Simple answer to my own question for the quick reader: vor.ridge_vertices provides the indices into the vor.vertices array to get the edges. – Prager

Answer 1

Take a look at the ridge_vertices attribute:

    ridge_vertices  (list of list of ints, shape (nridges, *))
        Indices of the Voronoi vertices forming each Voronoi ridge.

Each element in that list is a pair of integers. Each integer is an index into the vertices list. So each element defines a line to be draw in the Voronoi diagram. An index of -1 means a point that is "at infinity".

Here's script that draws the lines of the Voronoi diagram:

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


points = np.array([[0, 0], [0, 1], [0, 2],
                   [1, 0], [1, 1], [1, 2],
                   [2, 0], [2, 1], [2, 2]])

vor = Voronoi(points)


fig = plt.figure()

# Mark the Voronoi vertices.
plt.plot(vor.vertices[:,0], vor.vertices[:, 1], 'ko', ms=8)

for vpair in vor.ridge_vertices:
    if vpair[0] >= 0 and vpair[1] >= 0:
        v0 = vor.vertices[vpair[0]]
        v1 = vor.vertices[vpair[1]]
        # Draw a line from v0 to v1.
        plt.plot([v0[0], v1[0]], [v0[1], v1[1]], 'k', linewidth=2)

plt.show()

It creates:

Unsnap

Wonderful! For future viewers, the primary insight is that vor.ridge_vertices provides the indices into the vor.vertices array and that's how you get the edges! Fantastic. Thanks. – Prager

Thank you so much! I just found that plt.hold(True) is deprecated and the call would be superfluous. Source: link – Briarwood

@Martin, thanks for letting me know about the deprecation of hold(True). I removed it from the code. – Unsnap