Poisson disk patterns

Back to computer graphics

A poisson disk pattern is characterized by the property that every two points have at least a chosen delta distance between them. A poisson disk pattern to which no point can be added is called maximal. Up until recently there were no known efficient algorithms for the generation of maximal poisson disk patterns. Nowadays algorithms run in linear time and space for any dimension.

Below is a maximal 1D poisson disk pattern with a minimum distance of 5 pixels. For visualization, I have made the point vertical lines.

Below is a maximal 2D poisson disk pattern with a minimum distance of 5 pixels.

Below is a maximal 3D poisson disk pattern with a minimum distance of 35 pixels. For visualization, the points farther away are shaded darker and orthogonally projected on the screen.

Below is a maximal 4D poisson disk pattern with a minimum distance of 70 pixels. For visualization, the 4d points are shaded by their depth and colored by their fourth coordinate.