  We present a new algorithm for the automatic one-shot generation of scattered
node sets on irregular 2D and 3D domains using Poisson disk sampling coupled to
novel parameter-free, high-order parametric Spherical Radial Basis Function
(SBF)-based geometric modeling of irregular domain boundaries. Our algorithm
also automatically modifies the scattered node sets locally for time-varying
embedded boundaries in the domain interior. We derive complexity estimates for
our node generator in 2D and 3D that establish its scalability, and verify
these estimates with timing experiments. We explore the influence of Poisson
disk sampling parameters on both quasi-uniformity in the node sets and errors
in an RBF-FD discretization of the heat equation. In all cases, our framework
requires only a small number of "seed" nodes on domain boundaries. The entire
framework exhibits O(N) complexity in both 2D and 3D.
