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

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

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

sites

Explode

Automatic explosion

Exploding speed

Transparency

depthWrite

Rotation

x-axis

y-axis

z-axis

Rotation speed

Display

Objects

Camera

SVG

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

> 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
> 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