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GeoVoronoi (and GeoDelaunay)

Christopher Wolfram, WOLFRAM
Posted 5 years ago

An example of a GeoVoronoi

POSTED BY: Christopher Wolfram
8 Replies
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POSTED BY: Richard Hennigan
J. M.
J. M.
Posted 5 years ago

This is very nice. I note that the spherical Voronoi implementation in my posts was written quite a while ago, and using undocumented properties like "VertexFaceConnectivity" was the easiest method. Nowadays, I would say it's more advisable to use MeshConnectivityGraph[]:

With[{mcg = MeshConnectivityGraph[chm, {2, 0}, 0]},
     Table[EdgeList[mcg, DirectedEdge[_, {0, k}]][[All, 1]][[All, 2]],
           {k, MeshCellCount[chm, 0]}]]

but of course you should do your own comparisons against your DualPolyhedron[] approach.

A good survey paper to read about all these things is this paper by Sugihara, which has also nice pointers to other literature.
POSTED BY: J. M.
J. M.
J. M.
Posted 5 years ago

I agree; in a sense, that's what made the undocumented functions a little more convenient to use, since they were (apparently) orientation-preserving. In the planar case, you can do a reconstitution with ConvexHullMesh[], but it is murkier in the spherical case.
POSTED BY: J. M.
POSTED BY: Christopher Wolfram

Ah, that makes a lot of sense. You are basically getting only the "outer" hull (a bit like the upper/lower hull) instead of the full convex hull. I'll make that change if I submit these to the function repository.

Edit: I wonder why GeoVoronoi seems to work without that extra vertex.
POSTED BY: Christopher Wolfram

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POSTED BY: EDITORIAL BOARD
J. M.
J. M.
Posted 5 years ago

That's because Voronoi already naturally wraps around, similar to how a planar Delaunay is bounded, but a planar Voronoi covers all of the plane.
POSTED BY: J. M.

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