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Any theory for the minimum distance expected between n evenly spaced
points on a sphere?
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Greg M. Johnson <"gregj;-)56590\""@aol.c;-)om> wrote:
: Any theory for the minimum distance expected between n evenly spaced
: points on a sphere?
Define "evenly spaced".
--
main(i,_){for(_?--i,main(i+2,"FhhQHFIJD|FQTITFN]zRFHhhTBFHhhTBFysdB"[i]
):_;i&&_>1;printf("%s",_-70?_&1?"[]":" ":(_=0,"\n")),_/=2);} /*- Warp -*/
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"Greg M. Johnson" wrote:
>
> Any theory for the minimum distance expected between n evenly spaced
> points on a sphere?
http://www.math.niu.edu/~rusin/papers/known-math/index/spheres.html
--
Ken Tyler - 1400+ POV-Ray, Graphics, 3D Rendering, and Raytracing Links:
http://home.pacbell.net/tylereng/index.html http://www.povray.org/links/
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Warp wrote:
> Greg M. Johnson <"gregj;-)56590\""@aol.c;-)om> wrote:
> : Any theory for the minimum distance expected between n evenly spaced
> : points on a sphere?
>
> Define "evenly spaced".
as far apart as they goin' to git on the surface given a diminishing rate of
return in an iterative algorithm that puts them further and further apart.
I was actually hoping for a table, so I could check my algorithm for evenly
spacing points on a sphere. I was using a method I saw from (Paul Bourke?)
which was painstakingly slow. I later just applied the flocking repulsion
algorithm and got good results after a dozen iterations.
The most relevant page I found from Ken's link was at
http://www.math.niu.edu/~rusin/papers/known-math/96/sph.rand
All this stuff was just out of reach for me mathematically, although I don't
know why.
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How's this for a theory. The average distance between any of N points and
one of its neighbors should be about the square root of 1/N of the surface
area of the sphere.
Making it into a theorem is left as an excercise for the reader.
"Greg M. Johnson" <"gregj;-)56590\""@aol.c;-)om> wrote in message
news:39ce9f7e@news.povray.org...
> Any theory for the minimum distance expected between n evenly spaced
> points on a sphere?
>
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