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 4.13, release 4.12, 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
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;
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