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From: Raphael on 3 May 2010 06:53
What if the bounding surface is not convex ? The MPT toolbox only deals with convex polytopes, I think.

I have a point cloud in 3D representing spatial positions of cell nuclei of an embryo. The overall shape is not convex (it's actually a sort of thick spherical cap). I got a tight tessellation of it through a ball-fretting algorithm (http://www.mathworks.com/matlabcentral/fileexchange/24619-surface-recostruction-from-scattered-points-cloud-part3 ), which I fed with a Delaunay tessellation.

Now I would like a Voronoi diagram bounded by this tight tessellation. How should I do this ?

The point is getting estimations of cell density (taking borders into account), neighbourhood relationships, volume estimation, etc.

Do you think the strategy is a good one ?

By the way, I guess there is a great deal of literature on the robustness of Voronoi diagrams. Since the positions of my cell nuclei are a little noisy and do not represent very well the whole cells, obviously, is there a way to compute a "robust" Voronoi diagram ? What are centroidal Voronoi diagrams, which I heard about, exactly ?

Thank you in advance,
Raphaël
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