POV-Ray : Newsgroups : povray.advanced-users : How to distribute points equally on sqhere surface? : Re: How to distribute points equally on sqhere surface? Server Time
30 Jul 2024 20:31:08 EDT (-0400)
  Re: How to distribute points equally on sqhere surface?  
From: Mark Gordon
Date: 3 Jun 1999 22:24:35
Message: <37572AFC.CE6EC6F9@mailbag.com>
Peter Santo wrote:
> 
> Is there an exact solution for 5, 7 or 16 points?

IIRC from my chemistry days (one of the real-world applications of this
stuff), the solution for 5 points is (in terms of the surface of a
sphere) three on the equator, 120 degrees apart, and the other two at
the poles.

I'm not sure about 7 or 16.  I get the impression that exact solutions
exist for all values of n.  It boils down to a big optimization problem,
if you construct it in terms of minimizing net forces among a set of
mutually repellant points constrained by a sphere.  Maybe linear
programming would yield solutions?

-- 
Mark Gordon
mtg### [at] povrayorg


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