Hi there,


I've got a little problem: i want to arrange a number of little
spheres (or dots) on the surface of a big sphere. The tricky thing
is that they should have all the same distance to each other.
Is there a mathematical algorithm to calculate the 3d vectors
for these dots?


thanks,
Christian Grieger

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> I've got a little problem: i want to arrange a number of little
> spheres (or dots) on the surface of a big sphere. The tricky thing
> is that they should have all the same distance to each other.
> Is there a mathematical algorithm to calculate the 3d vectors
> for these dots?

There are several approaches to this problem, here's a link:

http://www.math.niu.edu/~rusin/known-math/index/spheres.html

(shameless plug follows:)
But you might also want to have a look at my Electrostatic Repulsion Macro,
downloadable from my website...
http://www.nolights.de

Regards,
Tim
-- 
"Tim Nikias v2.0"
Homepage: <http://www.nolights.de>

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> There are several approaches to this problem, here's a link:
> http://www.math.niu.edu/~rusin/known-math/index/spheres.html
> 
> But you might also want to have a look at my Electrostatic Repulsion Macro,
> downloadable from my website... http://www.nolights.de

thanks, thats exactly what i want!  :)


-- 
christian grieger
system developer
triplex IT solutions

triplex GmbH
herzog-heinrich-strasse 11-13
D-80336 munich

tel +49 89 209138-44
fax +49 89 209138-10

chr### [at] triplexde
www.triplex.de

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A similar question was asked recently (1st March) in p.general under
"Sphere/polyherdon question" (sic). Conclusions reached were the same as
here (random allocation, electrostatic repulsion) but there was also some
discussion about some other algorithms if you're interested.

-Chris




"Christian Grieger" <chr### [at] triplexde> wrote in message
news:40A33372.FD5D4F77@triplex.de...
> Hi there,
>
>
> I've got a little problem: i want to arrange a number of little
> spheres (or dots) on the surface of a big sphere. The tricky thing
> is that they should have all the same distance to each other.
> Is there a mathematical algorithm to calculate the 3d vectors
> for these dots?
>
>
> thanks,
> Christian Grieger

Post a reply to this message

"Christian Grieger" <chr### [at] triplexde> wrote in message
news:40A33372.FD5D4F77@triplex.de...
|
| I've got a little problem: i want to arrange a number of
| little spheres (or dots) on the surface of a big sphere.
| The tricky thing is that they should have all the same
| distance to each other. Is there a mathematical algorithm
| to calculate the 3d vectors for these dots?
|

What do you mean by "a number"? What do you mean by "the same distance"?
If you mean a large number then these algorithms are going to take a
very long time to use. If you can live with the dots being very close to
(close enough for visual inspection), but not exactly the same distance
from each other, then there are much simpler ways. Subdivision of a
polygon will give results very quickly, though you will not have exact
control over the number of dots nor will they all technically have the
same distance from each other (though they will be very close).

 -Shay

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Christian Grieger <chr### [at] triplexde> wrote:
> I've got a little problem: i want to arrange a number of little
> spheres (or dots) on the surface of a big sphere. The tricky thing
> is that they should have all the same distance to each other.

  There's only one arrangement of 4 points which meets this requirement:
The vertex points of a regular tetrahedron. (Technically speaking it's
also possible with 3 points, placing them at the vertices of an equilateral
triangle).
  It's not possible to arrange more than 4 points in such a way that the
distance is equal between them.

  Of course you didn't mean this, and thus your definition is wrong.
What you meant was something like an arrangement of points such that
the distance from a point to n of its closest neighbour points is always
equal.
  Unfortunately this isn't possible but for a very limited amount of
points (basically regular polyhedron vertices and perhaps a couple of
other shapes).

  What you want is an algorithm which tries to maximize the distance
between the points on the surface of a sphere. Even though it's only
an approximation, it usually looks good enough. The other replies should
help on this matter.

-- 
#macro M(A,N,D,L)plane{-z,-9pigment{mandel L*9translate N color_map{[0rgb x]
[1rgb 9]}scale<D,D*3D>*1e3}rotate y*A*8}#end M(-3<1.206434.28623>70,7)M(
-1<.7438.1795>1,20)M(1<.77595.13699>30,20)M(3<.75923.07145>80,99)// - Warp -

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