Based on the last approach on this page, you can simply generate a vector consisting of independent samples from three standard normal distributions, then normalize the vector such that its magnitude is 1: import numpy as np def sample_spherical(npoints, ndim=3): vec = np.random.randn(ndim, npoints) vec /= np.linalg.norm(vec, axis=0) return vec For example: from matplotlib import … Read more
While I prefer the discarding method for spheres, for completeness I offer the exact solution. In spherical coordinates, taking advantage of the sampling rule: phi = random(0,2pi) costheta = random(-1,1) u = random(0,1) theta = arccos( costheta ) r = R * cuberoot( u ) now you have a (r, theta, phi) group which can … Read more
I see the mistake so often, the suggestion that to generate random numbers with a given sum, one just uses a uniform random set, and just scale them. But is the result truly uniformly random if you do it that way? Try this simple test in two dimensions. Generate a huge random sample, then scale … Read more