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Re: Convex random polyhedrons

• To: mathgroup at smc.vnet.net
• Subject: [mg85219] Re: Convex random polyhedrons
• From: Antti Penttilä@smc.vnet.net
• Date: Sat, 2 Feb 2008 03:30:50 -0500 (EST)
• Organization: University of Helsinki
• References: <fnuhk1$9us$1@smc.vnet.net>

Hi,

I suspect that it would be quite difficult to create random convex 
polyhedrons with exact number of n points. What I have done is that I 
have created a large number of random, possibly non-convex polyhedrons 
by sampling k points in spherical coordinates with random distance r 
from origin, and with random angles. After that I have computed the 
convex shape for each polyhedron. Some of the points in the original 
polyhedron will be left out in the convex version.

Antti

Steve Gray wrote:
> 	Does anyone have a handy way in Mathematica of making convex random
> polyhedrons in 3D? The number of points should be a parameter. The
> points do not have to be evenly spaced (obviously) and if up to say
> 10% of them are not quite convex, that's ok. I have some ideas but
> maybe it's already been done. 
> 	I know about ConvexHull3D.m and maybe that's the best way, but
> it doesn't return the number of points, which must be computed. That
> seems inefficient because the number of points must be exact.
> 
> Steve Gray
>