Peter Santo <san### [at] poolinformatikrwth-aachende> wrote:
> Hello!
>
> I would like to render a sphere with an arbitrary number of points (or
> smaller spheres) on its surface that I want to distribute equally (so
> the distance to the neighbouring points is nearly equal for every
> point). I suppose there is no perfect solution for that problem, but I
> would like to approximate it as good as possible.
>
> A funktion could look like this:
> Input: Number of points (n)
> Output: n pairs of angles (horizontal and vertical from sphere's center)
> that describe the location of the points. (alternatively <x,y,z>-coords
> on the surface)
>
> Of course, the solution is easy for n = 1(trivial), 2(line),
> 3(traingle), 4(tetrahedron), 6(octahedron), 8(cube) and some more. I
> also checked http://www.cris.com/~rjbono/html/domes.html , but geodesic
> domes always have a "magic" number of corners.

There are only 3 solutions because when all points are equaly distributed
they will make out triangles with equaly long sides, and there only exists 3
such cases: the tetrahedron(4 sides), the octahedron(8 sides) and the
dodecaedron(20 sides). On a cube, for example, the points are not equaly
distributed. How ever there are recursive methods of finding a close
solution for any number of points, and that usualy is close enough. Two
methods are described in this page:
http://www.mhri.edu.au/~pdb/geometry/spherepoints/index.html

/Anders

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