From: "Robert Phillips" <>
Newsgroups: comp.soft-sys.matlab
Subject: Re: Shortest distance from point to ellipsoid surface
Date: Mon, 11 Jul 2011 00:38:09 +0000 (UTC)
Organization: Embry-Riddle Aeronautical University
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Thank you for replying,

I apologize for not specifying; my grid of 3-D points usually contains between 25,000 and 50,000 "interior points". Usually I'll generate (200+1)^2 points using the mesh command, and then they're "filtered" by checking if they lie inside of an asteroid.

I'm improving a self-made finite element analysis program for simulating gravitational fields of asteroids. The primary goal is to use the fewest sphere and/or ellipsoid elements as possible; hence, the goal becomes defining the largest possible elements inside of the asteroid.

I've aced the sphere element technique without needing to generate sphere surface points, but I'm trying to optimize my ellipsoid element technique.

I haven't used the Image Processing Toolbox before, so I'll have to dig around and familiar myself with bwdist.

I'm trying to find the largest possible ellipsoid inside of an asteroid (of arbitrary shape: convex, concave, etc.). I need to assign to each interior point its minimum distance from itself to a previously-defined ellipsoid surface. It would take a while to explain why I need these distances lol.

The vectors of and distances from the ellipsoid center to all interior points are calculated for other uses. If those vectors are the same vectors along which the minimum distance would be found, but if they were, I'm sure that they could be parametrized and solved in conjunction with the ellipsoid surface equation.

And yes Roger has helped me a TON before, and I truly appreciate all of your help!