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 Lorenzo

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 > > ______________________________________________ > R-help at 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.

"Lorenzo Isella" <lorenzo.isella at 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