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I am facing a problem as follows : I want to make poisson voronoi diagram & for this I have to appropriately choose some generating points. Sources on internet(WIKI) refers that these points have to be obtained from poisson processes. So, how can I go about doing this in Mathematica? [I have little exposure to Poisson processes or for that matter any other process.]

Madhusudana
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  • The idea is relatively simple: in two dimensions, if you have a square region, split it into "cells", associate each cell with a Poisson-distributed random integer (call it $k$), and generate $k$ points in that cell with the coordinates drawn from a uniform distribution. – J. M. ain't a mathematician Jun 10 '15 at 10:44
  • @Guesswhoitis. could you please elaborate a bit more on creation of "cells". – Madhusudana Jun 10 '15 at 10:53
  • You just cut the square into $n\times n$ smaller squares, for some $n$. – J. M. ain't a mathematician Jun 10 '15 at 10:56
  • @Guesswhoitis. then what are u trying to convey via 'generate k points'. k is the name to denote the RV(that's what I got). Please clarify – Madhusudana Jun 10 '15 at 11:02
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    The output of RandomVariate[PoissonDistribution[(* stuff *)]] is an integer, right? That is the number of points you need to generate in the cell that number is associated with. – J. M. ain't a mathematician Jun 10 '15 at 11:06
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    It seems that this question isn't really about Mathematica but about understanding what "Poisson process" means, especially in 2D. – Szabolcs Jun 10 '15 at 11:43

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vMesh = VoronoiMesh[
   myPts = RandomVariate[UniformDistribution[{{0, 1}, {0, 1}}], 50]];
Show[vMesh, Graphics[Point /@ myPts]]

enter image description here

David G. Stork
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