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 >