[R] Test for Random Points on a Sphere

[Lorenzo Isella]

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