Theoretical guarantees for poisson disk sampling using pair correlation function

In this paper, we study the problem of generating uniform random point samples on a domain of d dimensional space based on a minimum distance criterion between point samples (Poisson-disk sampling or PDS). First, we formally define PDS via the pair correlation function (PCF) to quantitatively evaluate properties of the sampling process. Surprisingly, none of the existing PDS techniques satisfy both uniformity and minimum distance criterion,...