[R] Test for Random Points on a Sphere

Nordlund, Dan (DSHS/RDA) NordlDJ at dshs.wa.gov
Fri Oct 5 20:40:29 CEST 2012

> -----Original Message-----
> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-
> project.org] On Behalf Of R. Michael Weylandt
> Sent: Friday, October 05, 2012 11:17 AM
> To: Lorenzo Isella
> Cc: r-help at r-project.org
> Subject: Re: [R] Test for Random Points on a Sphere
> On Fri, Oct 5, 2012 at 5:39 PM, Lorenzo Isella
> <lorenzo.isella at gmail.com> wrote:
> > 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?
> > Many thanks
> >
> Gut says to divide the surface into n bits of equal area and see if
> the points appear uniformly in those using something chi-squared-ish,
> but I'm not aware of a canonical way to do so.
> Cheers,
> Michael
> > Lorenzo
> >

I would be more inclined to use a method which is known to produce a points uniformly distributed on the surface of a sphere and not worry about testing your results.  You might find the discussion at the following link useful.


Hope this is helpful,


Daniel J. Nordlund
Washington State Department of Social and Health Services
Planning, Performance, and Accountability
Research and Data Analysis Division
Olympia, WA 98504-5204

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