> -----Original Message----- > From: r-help-boun...@r-project.org [mailto:r-help-bounces@r- > project.org] On Behalf Of R. Michael Weylandt > Sent: Friday, October 05, 2012 11:17 AM > To: Lorenzo Isella > Cc: r-help@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.ise...@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. http://mathworld.wolfram.com/SpherePointPicking.html Hope this is helpful, Dan Daniel J. Nordlund Washington State Department of Social and Health Services Planning, Performance, and Accountability Research and Data Analysis Division Olympia, WA 98504-5204 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
