Voronoi Diagrams

This tutorial is probably also available as a Jupyter notebook in the demo folder in the polymake source and on github.

Different versions of this tutorial: latest release, release 4.11, release 4.10, release 4.9, release 4.8, release 4.7, release 4.6, release 4.5, release 4.4, release 4.3, release 4.2, release 4.1, release 4.0, release 3.6, nightly master

This is an old revision of the document!

Voronoi diagrams are constructed from their sites (given in homogeneous coordinates).

$VD = new VoronoiDiagram(SITES=>[[1,1,1],[1,0,1],[1,-1,1],[1,1,-1],[1,0,-1],[1,-1,-1]]);
$VD->VISUAL_VORONOI;

Actually, via lifting to the standard paraboloid, Voronoi diagrams are derived from Polytope. That's why they have VERTICES, FACETS, and such.

polytope > print $VD->FACETS;
2 -2 -2 1
1 0 -2 1
2 2 -2 1
2 -2 2 1
1 0 2 1
2 2 2 1
1 0 0 0

polytope > print $VD->VERTICES;
0 0 1 2
0 1 0 2
1 1/2 0 -1
0 -1 0 2
0 0 -1 2
1 -1/2 0 -1