From: dmd1@lehigh.edu (DON DAVIS) Subject: responses re points on sphere Date: Mon, 07 Aug 2000 08:25:19 EDT Newsgroups: [missing] To: Distribution.List@lehigh.edu (toplist) Summary: [missing] From: Dave Rusin Date: Sun, 6 Aug 2000 14:10:00 -0500 (CDT) Subject: Re: question from physicist The question about distributing points evenly on spheres shows up regularly on discussion groups like USENET's sci.math, so I wrote up a FAQ to address this and a few related questions. You can direct people to this page: index/spheres.html Of course there is no "even" way to distribute N points in general. I don't even think it's true that there is a unique equilibrium configuration of points moving under electrostatic repulsion. Tables have been computed showing configurations of various numbers of points. dave __________________________________________________ Date: Sun, 06 Aug 2000 19:34:24 -0400 From: Dan Christensen Subject: Re: question from physicist > It starts with a physical problem: What is the minimum-energy > configuration of n>1 identical particles of equal charge, constrained to > move on the surface of a sphere? This question is often asked in computer graphics newsgroups. One FAQ for this topic can be found by following the first link on index/spheres.html which has other useful information. The potential energy measure of dispersion is called D3 there, and isn't treated in any detail, since there is in general no simple answer to this question. For even more information, search on google for "points sphere": http://www.google.com/search?q=points+sphere+ For example, the page http://www.swin.edu.au/astronomy/pbourke/geometry/spherepoints/ (the first that comes up) gives C code for an approximate algorithm. Dan