How about drawing a 3D shape (depending upon the value of N) with equal
distances between neighbour nodes and equal angles between the edges? All the
nodes lie on the imaginary sphere and the distance to the center is the same.
Thus you get one and only one shape for each value of N. You can rotate it
inside the sphere.
How about putting them randomly on that sphere? Or use one of the well-known
distributions (Poisson distribution for example)? (use 3 coordinate versions of
What about using a random/stochastic process (Markov, for instance). (use 3
coordinate version of these processes)
Greg McCarroll wrote:
> I was working on my talk for YAPC::Europe and I got a little distracted,
> with the following problem and I also thought some of you might like to
> think about it.
> First of all, consider the problem of distributing N points around the
> origin evenly in 2D, so they are all the same distance from the origin.
> Now this is quite easy, you can simply imagine a circle and the points
> placed around the circle, each 360/N degrees apart in terms of projections
> from the origin.
> Simple huh?
> Ok, now how can you distribute N points around the origin in _3_ dimensions,
> again all of them at the same distance from the origin? Obviously
> there will be an imaginary sphere again, but where do you put the points.
> Thoughts are welcome, i'm currently trying to solve it and having
> lots of gotchas. However if you have a complete solution please put
> in some *spoiler* space.
> Greg McCarroll http://220.127.116.11/~gem/
Department of Communication Technology
Aalborg University of Technology