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, simultaneously.
These approaches typically create an approximate PDS with
high regularity, and inherently present high risk for sample aliasing.
Our new formulation based on PCF introduces a new approach to
evaluate PDS properties which leads to theoretical bounds on the
size of a PDS in arbitrary dimensions as well as a faster algorithm to
create better quality samplings than the current PDS approaches.