user_guide:tutorials:master:voronoi

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 4.7, 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;
sites
Explode
Automatic explosion
Exploding speed
Transparency
depthWrite
Rotation
x-axis
y-axis
z-axis
Rotation speed
Display
Objects
Camera
SVG
Download
New tab

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
  • user_guide/tutorials/master/voronoi.txt
  • Last modified: 2022/04/07 04:58
  • (external edit)