I believe that this is a doc error in V10 (this was programmed to be but not implemented). The new VoronoiMesh should work for 3D set of points.

The DelaunayMesh function works. Here is a doc example:

pts = RandomReal[{-1, 1}, {25, 3}];
DelaunayMesh[RandomReal[{-1, 1}, {25, 3}]]

enter image description here

But if you try:

pts = RandomReal[{-1, 1}, {25, 3}];

You get the error: enter image description here

Docs for Voronoi say:

The cells will be intervals in 1D, convex polygons in 2D, and convex polyhedra in 3D.

Tested in V10.0.0 for Mac and Win.


marked as duplicate by J. M. is away Feb 24 at 2:49

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    $\begingroup$ I have already talked about this here. I'm not so sure it is a bug, rather it has not been implemented but planned. Because internally the new Mesh functions rely on TetGen which supports 3D voronoi diagrams but somehow this functionality has been omitted. $\endgroup$ – RunnyKine Jul 15 '14 at 0:02
  • $\begingroup$ @Szabolcs no! Typo. $\endgroup$ – Murta Jul 15 '14 at 0:14
  • $\begingroup$ Not implemented in V10.0.1 yet $\endgroup$ – Murta Sep 17 '14 at 1:38
  • $\begingroup$ I didn't expect it to be implemented. When I asked about it in one of the online seminars they had, their response made me believe it will come in V11 or later. $\endgroup$ – RunnyKine Sep 17 '14 at 2:18

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