Voronoi Diagrams – How to Create Random Voronoi Diagrams

Question

I'm interested in what research has already been done with regards to the statistics of random voronoi diagrams. I have had a look on google scholar and results are a little inconclusive. I'm interested in things like the expected size of Voronoi cells etc.

Answer 1

The number of $(d{-}1)$-facets of a Poisson-process Voronoi cell in $\mathbb{R}^d$ is: $6$ for $d{=}2$; $\approx 15.5$ for $d{=}3$; and $\approx 37.8$ for $d{=}4$. For references and other stats, see:

Masaharu Tanemura, "Random Voronoi Cells of Higher Dimensions." (link).

Here is an unrelated but attractive image from www.qhull.org:

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  ^{Voronoi image by KOOK Architecture, Silvan Oesterle and Michael Knauss.}