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Re: Random direction using space partitioning?

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On Wed, 05 Jun 2019 07:04:56 -0400, Richard Damon vomited this verbiage
that I considered to be worthy of my attention for one of a variety of
possible reasons:

> 
>  but if
> you want to maintain uniformness, you need to be very careful how you do
> the transform
>

That's what the Jacobian is for.

The determinant of the Jacobian of the spherical transform will define
the PDF of the desired distribution.  Then the Inverse CDF Method is used
to relate a uniform distribution to the that PDF.

Now see if you can solve this one:

Instead of uniformly sampling points on a spherical surface, uniformly
sample points inside the spherical ball centered on the origin.  In this
case we have 3 degrees of freedom and 2 areas of clustering.

The Jacobian determinant is R^2 * sin(phi)

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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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