An -radius poisson-disk pattern in , , is a point-set for which it holds that the minimum distance between the points in is at least , with the metric chosen freely. Such point-sets are said to satisfy the poisson-disk property. If no point can be added to without breaking the poisson-disk property, the pattern is called maximal. Maximal poisson-disk patterns are of more interest because otherwise a single point would satisfy the requirements for any and non-empty .
Pastel implements an algorithm to generate almost-maximal poisson-disk patterns inside a rectangular region in . The ‘almost’ is the consequence of using an algorithm that is based on randomization.
Here are maximal poisson-disk patterns in and .
Fast Poisson-Disk Sampling in Arbitrary Dimensions, Robert Bridson, Siggraph 2007.