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Re: Random direction using space partitioning?

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luser droog <luser.droog@gmail.com> writes:

> I had an idea about an algorithm for generating random
> unit vectors. Instead of mapping 2 or 3 random numbers
> to coordinates and then constraints and whatnot, ...
> what I we set up a 1D->3D mapping straight from a single
> number? In essence, the idea is to do something like a
> Hilbert Space Curve that does the same form of mapping,
> https://en.wikipedia.org/wiki/Hilbert_curve, but using
> a curve that is by definition constrained to the surface
> we want.

I feel sure that can work, but I am not si sure that it will be at all
easy and the problem is not really intrinsically hard.

Mind you, as you say,

> space [filling] curves are cool

so I'd like to see such a solution.

However, I'm having trouble coming up with a space filling curve that is
(a) constrained to the unit sphere, (b) uniformly dense on it and (c)
has a form that allows a point to be readily computed.  (Other than
mapping a normal one onto an equal area projection of the sphere.)

I have a feeling this will be an entertaining but futile avenue.

-- 
Ben.

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Thread

Random direction using space partitioning? luser droog <luser.droog@gmail.com> - 2019-06-04 19:35 -0700
  Re: Random direction using space partitioning? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-06-05 04:25 +0100
    Re: Random direction using space partitioning? Clifford Heath <no.spam@please.net> - 2019-06-05 13:30 +1000
  Re: Random direction using space partitioning? John Forkosh <forkosh@panix.com> - 2019-06-05 04:36 +0000
    Re: Random direction using space partitioning? Richard Damon <Richard@Damon-Family.org> - 2019-06-05 07:04 -0400
      Re: Random direction using space partitioning? "F. Russell" <frussell@random.info> - 2019-06-05 12:55 +0000

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