Voronoi Diagram Explanation

Question

I am trying to generate Voronoi split polygons and not able to understand the parameter 'furthest_site=True' in Voronoi's Scipy's implementation.

from scipy.spatial import Voronoi, voronoi_plot_2d

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

vor = Voronoi(points,furthest_site=True)

import matplotlib.pyplot as plt

fig = voronoi_plot_2d(vor) plt.show()

This gives me output as :

What is the explanation for attribute "furthest_site=True"

Answer 1

scipy says it uses QHull to compute voronoi diagrams, and they have this in their documentation:

The furthest-site Voronoi diagram is the furthest-neighbor map for a set of points. Each region contains those points that are further from one input site than any other input site.

Furthest (or "farthest")-site diagrams are described in plenty of other places, including example diagrams; for example, in other stackexchange posts: 1, 2.

Your plot looks odd because your pointset is somewhat degenerate; only the four corner points ever serve as the furthest reference point.