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Geometry Wolfram Language

Cell indices and cell coordinates from Voronoi diagram

Sander Huisman

Sander Huisman, University of Twente

Posted 9 years ago

Dear All, Let's say I have a Voronoi diagram of some points: voronoidata=VoronoiMesh[0.5+{{9,86},{89,64},{28,49},{21,47},{31,70},{6,36},{3,24},{68,75},{25,55},{47,21}}] this will get me the Voronoi mesh: I know I can do `MeshCoordinates[voronoidata]` to get the coordinates of the mesh. How do I get the indices to make the polygons: basically what I want are the indices: ToExpression[StringReplace[ToString[voronoidata//FullForm],"MeshRegion"->"List"]][[2]] {Polygon[{{11, 6, 10, 2}, {18, 4, 13, 22}}], Polygon[{{16, 9, 17, 20, 21}, {1, 3, 7, 2, 10}, {5, 1, 10, 6,8}, {15, 11, 2, 7, 14}, {13, 4, 5, 8, 12}, {14, 7, 3, 9, 16}}], Polygon[{{19, 12, 8, 6, 11, 15}}], Polygon[{{17, 9, 3, 1, 5, 4, 18}}]} I would consider this to be a 'hack' as voronoidata is an atom, however the data can still be seen by FullForm(?) This procedure is however a bit cumbersome as you understand...

POSTED BY: Sander Huisman

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Jaebum Jung

Jaebum Jung, Wolfram

Posted 9 years ago

MeshCells[voronoidata, 2] {Polygon[{11, 6, 10, 2}], Polygon[{18, 4, 13, 22}], Polygon[{16, 9, 17, 20, 21}], Polygon[{1, 3, 7, 2, 10}], Polygon[{5, 1, 10, 6, 8}], Polygon[{15, 11, 2, 7, 14}], Polygon[{13, 4, 5, 8, 12}], Polygon[{14, 7, 3, 9, 16}], Polygon[{19, 12, 8, 6, 11, 15}], Polygon[{17, 9, 3, 1, 5, 4, 18}]}

MeshCells[voronoidata, 2]
{Polygon[{11, 6, 10, 2}], Polygon[{18, 4, 13, 22}],   Polygon[{16, 9,
17, 20, 21}], Polygon[{1, 3, 7, 2, 10}],   Polygon[{5, 1, 10, 6, 8}],
 Polygon[{15, 11, 2, 7, 14}],   Polygon[{13, 4, 5, 8, 12}],
 Polygon[{14, 7, 3, 9, 16}],   Polygon[{19, 12, 8, 6, 11, 15}],
 Polygon[{17, 9, 3, 1, 5, 4, 18}]}

POSTED BY: Jaebum Jung