I'm looking for some material to gain a better understanding about Poisson disk sampling. Specifically I would like to understand how a point is generated, and since I'm using it to generate points inside a rectangular 2D area, I'd like to gain knowledge about what's the probability distribution from which the points are sampled (e.g. how close is it to be uniform? Does any point share the same probability to be selected? I would be tempted to say that each point has a null probability to be selected, in which case I'm interested in the probability density function of the distribution from where samples are taken).
I searched online a bit and unfortunately the web world seemed to me to be pretty avid of material about it. All I could find was papers discussing algorithmic strategies to efficiently implement it on a computer. I'm more interested in the mathematical aspect of it as of now.
Any resource about the topic is definitely appreciated, thanks in advance.