Blue noise sampling using an SPH-based method

Abstract

We propose a novel algorithm for blue noise sampling inspired by the Smoothed Particle Hydrodynamics (SPH) method. SPH is a well-known method in fluid simulation - it computes particle distributions to minimize the internal pressure variance. We found that this results in sample points (i.e., particles) with a high quality blue-noise spectrum. Inspired by this, we tailor the SPH method for blue noise sampling. Our method achieves fast sampling in general dimensions for both surfaces and volumes. By varying a single parameter our method can generate a variety of blue noise samples with different distribution properties, ranging from Lloyd's relaxation to Capacity Constrained Voronoi Tessellations (CCVT). Our method is fast and supports adaptive sampling and multi-class sampling. We have also performed experimental studies of the SPH kernel and its influence on the distribution properties of samples. We demonstrate with examples that our method can generate a variety of controllable blue noise sample patterns, suitable for applications such as image stippling and re-meshing.