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From: "Bruno Luong" <b.luong@fogale.findmycountry>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Voronoi diagram on a sphere
Date: Fri, 6 Nov 2009 07:01:47 +0000 (UTC)
Organization: FOGALE nanotech
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"Abel Brown" <brown.2179@osu.edu> wrote in message <hd0e8h$c9$1@fred.mathworks.com>...
> iv been able to make voronoi diagrams easily on 2D plane but can not seem to get it right for a sphere.
> 
> iv googled around and found some spherical V. diagrams but cant seem to get matlab to do this
> 
> http://people.sc.fsu.edu/~%20burkardt/f_src/sxyz_voronoi/gen_00100.png
> 
> I have some points (lat, lon, ht  or x, y, z) and would like to make sphereical Voronoi diagram and plot it.  Any help would be awesome!
> 
> cheers! 

Voronoi cell is the "dual" of delaunay. 

Use convhulln on your (x,y,z) that gives something close to Spherical Delaunay (assuming the points are close enough to neglect the spherical curvature). Next draw the median line (on the sphere) separating each vertice its delaunay neighbor, the will form a polygonal of the voronoi cell. Do it repetitively for all vertices. 

Bruno