Sampling uniformly distributed random points inside a spherical volume

Question

I am looking to be able to generate a random uniform sample of particle locations that fall within a spherical volume.

The image below (courtesy of http://nojhan.fre

Answer 1

Normed gaussian 3d vector is uniformly distributed on sphere, see http://mathworld.wolfram.com/SpherePointPicking.html

For example:

N = 1000
v = numpy.random.uniform(size=(3,N)) 
vn = v / numpy.sqrt(numpy.sum(v**2, 0))