Hi Lorenzo,

Just a quick thought, the uniform probability density on a unit sphere is 1
/ (4pi),
what about binning those random points according to their directions and do
a chi-square test?

Regards,
Guo

On Sun, Oct 7, 2012 at 2:16 AM, <cberry@tajo.ucsd.edu> wrote:

> "Lorenzo Isella" <lorenzo.isella@gmail.com> writes:
>
> > Dear All,
> > I implemented an algorithm for (uniform) random rotations.
> > In order to test it, I can apply it to a unit vector (0,0,1) in
> > Cartesian coordinates.
> > The result is supposed to be a set of random, uniformly distributed,
> > points on a sphere (not the point of the algorithm, but a way to test
> > it).
> > This is what the points look like when I plot them, but other then
> > eyeballing them, can anyone suggest a test to ensure that I am really
> > generating uniform random points on a sphere?
>
> There is a substantial literature on this topic and more than one
> (metaphorical?) direction you could follow.
>
> I suggest you Google 'directional statistics' and start reading.
>
> Visit http://www.rseek.org and enter 'directional statistics' in
> the search box and click on the search button to see if there is
> something in R to meet your needs.
>
> A post to r-sig-geo might get more helpful responses once you can focus
> the question a bit more.
>
>
> HTH,
>
> Chuck
>
> > Many thanks
> >
> > Lorenzo
> >
>
> --
> Charles C. Berry                            Dept of Family/Preventive
> Medicine
> cberry at ucsd edu                          UC San Diego
> http://famprevmed.ucsd.edu/faculty/cberry/  La Jolla, San Diego 92093-0901
>
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