The Voronoi diagram is just the dual graph of the Delaunay triangulation. So, the edges of the Voronoi diagram are along the perpendicular bisectors of the edges of the Delaunay triangulation, so compute those lines. Then, compute the vertices of the Voronoi diagram by finding the intersections of adjacent edges. Finally, the edges are then … Read more
Update in July 2016: Thanks to a number of volunteers (especially Nikolai Nowaczyk and I), there is now far more robust / correct code for handling Voronoi diagrams on the surface of a sphere in Python. This is officially available as scipy.spatial.SphericalVoronoi from version 0.18 of scipy onwards. There’s a working example of usage and … Read more
The Voronoi data structure contains all the necessary information to construct positions for the “points at infinity”. Qhull also reports them simply as -1 indices, so Scipy doesn’t compute them for you. https://gist.github.com/pv/8036995 http://nbviewer.ipython.org/gist/pv/8037100 import numpy as np import matplotlib.pyplot as plt from scipy.spatial import Voronoi def voronoi_finite_polygons_2d(vor, radius=None): “”” Reconstruct infinite voronoi regions in … Read more
An easy algorithm to compute the Delaunay triangulation of a point set is flipping edges. Since a Delaunay triangulation is the dual graph of a Voronoi diagram, you can construct the diagram from the triangulation in linear time. Unfortunately, the worst case running time of the flipping approach is O(n^2). Better algorithms such as Fortune’s … Read more