On decompositional algorithms for uniform sampling from -spheres and -balls

We describe a universal conditional distribution method for uniform sampling from n -spheres and n -balls, based on properties of a family of radially symmetric multivariate distributions. The method provides us with a unifying view on several known algorithms as well as enabling us to construct novel variants. We give a numerical comparison of the known and newly proposed algorithms for dimensions 5, 6 and 7.