Densities separable in spherical coordinates have two advantages: i) the normalization constant is easy to compute, as the cumulative distribution can be decomposed into individual scalar integrals, and ii) an orthogonal inverse transform is directly available via a simple, scalar initial value problem and can be used to compute deterministic samples. We propagate uniform low-discrepancy sequences through that orthogonal inverse transform and obtain very homogeneous and even visually appealing deterministic samples. To demonstrate this technique, we exemplarily propose some spherical-coordinate-separable densities in S², R², and R³, including a non-isotropic modification of the von Mises-Fisher distribution. The proposed densities may be used, e. g. , to represent uncertain radar measurements and for directional estimation. Furthermore, the framework presented herein allows quite simple design of various more densities tailored to a given scenario.
Frisch et al. (Wed,) studied this question.