Uniform Spherical Distribution Generator

Generate uniformly random points within a sphere of dimension N

This function generates uniformly random points within a sphere of dimension N. It does this efficiently by inverting cumulative distribution functions, not by generating a uniform rectangular distribution and filtering away. This is particularly important for high dimensional spheres. In 6D for example, only one in twelve points generated in a 6D rectangle lies within the inner 6D sphere.
An example use-case of this function would be to initialize the positions and velocities of an ensemble of particles in three dimensions. In many physics simulations, it is common to perform such initializations independently for each dimension, which wastes processing power on uninteresting regions of phase-space near the corners of the 6D hypercube.