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Poisson disk sampling

Posted 1 year ago

 Poisson disk sampling -- various geometric regions

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POSTED BY: Denis Ivanov
7 Replies

The polycrystalline mesh regions at the end of this post are really appealing to me. So I applied my MeshVoronoiEntropy function which got recently published in Wolfram Function Repository https://resources.wolframcloud.com/FunctionRepository/resources/MeshVoronoiEntropy/

First, let's extract the bare mesh regions in order to apply MeshVoronoiEntropy function

meshstructs = MapThread[
   VoronoiMesh[First /@ #1, {{0., 1.}, {0., 1.}},
     MeshCellStyle -> {{2, All} -> LightYellow, {1, All} -> Brown},
     ImageSize -> 150] &,
   {data3, paramList}]; 

and I got the values for the corresponding Voronoi entropy, which is actually a form of Shannon entropy applied to polygon meshes as documented in Wolfram Function Repository.

This gives the Voronoi entropy for each mesh region.

meshVorEntr=ResourceFunction["MeshVoronoiEntropy"]/@meshstructs
{0.622363,0.575437,0.813453,1.09041,1.17685,1.28494}

The entropy is lowest for polycrystalline regions, as shown in the remastered grid picture

Grid[Partition[
MapThread[
Labeled[VoronoiMesh[First /@ #1, {{0., 1.}, {0., 1.}},
MeshCellStyle -> {{2, All} -> LightYellow, {1, All} -> Brown},
ImageSize -> 150], "Voronoi Entropy  " <> ToString@#2] &,
{data3, meshVorEntr}],
3]] 

Voronoi Entropy for different configurations

POSTED BY: Jessica Alfonsi
Posted 1 year ago

Take a look at the [Experimental] function HardcorePointProcess.

proc = HardcorePointProcess[30, 0.3, 2];
reg = Rectangle[{0, 0}, {10, 10}];
pts = RandomPointConfiguration[proc, reg];
Show[VoronoiMesh[pts[[1, 1]]], PlotRange -> {{0, 10}, {0, 10}}]

Voronoi mesh

POSTED BY: Jim Baldwin

I'm very glad that you found my contribution helpful for your research work. I will certainly have a look at this post in the forthcoming days and I would be really interested to have a look at your paper before submission.

POSTED BY: Jessica Alfonsi
Posted 1 year ago
POSTED BY: Denis Ivanov
POSTED BY: EDITORIAL BOARD
Posted 1 year ago

Thank you, but I’m glad I handled the details of the algorithm myself.
In addition, the parameter randomness will be useful for further research.
But I did not pay attention to Spatial Point Processes, they are also very useful, so thank you again!

POSTED BY: Denis Ivanov
POSTED BY: Jessica Alfonsi
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