  How to distribute a set of points uniformly on a spherical surface is a very
old problem that still lacks a definite answer. In this work, we introduce a
physical measure of uniformity based on the distribution of distances between
points, as an alternative to commonly adopted measures based on interaction
potentials. We then use this new measure of uniformity to characterize several
algorithms available in the literature. We also study the effect of optimizing
the position of the points through the minimization of different interaction
potentials via a gradient descent procedure. In this way, we can classify
different algorithms and interaction potentials to find the one that generates
the most uniform distribution of points on the sphere.
