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From: "Abel Brown" <brown.2179@osu.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Voronoi diagram on a sphere
Date: Fri, 6 Nov 2009 14:05:06 +0000 (UTC)
Organization: The Ohio State University
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hd0hkr$pq1$1@fred.mathworks.com>...
> "Abel Brown" <brown.2179@osu.edu> wrote in message <hd0e8h$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

Thanks for your reply Bruno

These points that I have are distributed all over the globe.  Some of the points are separated by thousands of kilometers so will not be able to neglect the spherical curvature.  

I was thinking to do some distance preserving projection on to a plane, do the V. diagram in 2D, and then map it back.  But in this case the polygons will not be "continuous".  The polygons at the edges will go off to infinity where as on a sphere all polygons will have a finite area.

Is there a way to use voronoin to do this?  this will do the 3D Voronoi diagram but need to plot the polygons on a sphere ...