A method for the generation of uniform point densities in samples that have an axis of symmetry and the Monte Carlo integration of functions whose domains have an axis of symmetry

Monte Carlo simulations are frequently employed to study samples that emit radiation. Often the first step in such a simulation is to generate a set of points in the sample volume such that radiation emanates from each point. In this work two methods are given in which uniform point densities are generated in samples with a symmetry axis. Stratified sampling schemes can be employed in both methods. In addition, both methods may be used to perform the Monte Carlo integration of a function whose domain occupies a volume that has a symmetry axis.