Point Picking

How To Choose Uniform and Isotropic Points

For many MC studies, it is desirable to select points that are uniform over a volume, and/or directions that are isotropic (no preferred direction). Here are some useful links explaining how to do this:

How to pick uniform points on a disk (for a cylindrical volume, do this and pick z uniform).
How to pick uniform points on a sphere to get an isotropic distribution.
(Remember that mathematician's phi is physicist's theta (zenith) and vice versa (azimuth.))