A method for generating uniform point distributions when the volume integral of a sample has constant integration limits in some curvilinear coordinate system

Monte-Carlo simulations are frequently employed to study samples that emit radiation. Often the first step in such a simulation is to generate a distribution of points in the sample volume such that radiation emanates from each point. In this work a method is given in which a uniform distribution of points may be generated in a sample whose volume integral, in some system of curvilinear coordinates, has constants for its limits of integration.