Stochastic point distributions with blue-noise spectrum are used extensively in computer graphics for various applications such as avoiding aliasing artifacts in ray tracing, halftoning, stippling, etc. In this paper we present a new approach for generating point sets with high-quality blue noise properties that formulates the problem using a statistical mechanics interacting particle model. Points distributions are generated by sampling this model. This new formulation of the problem unifies randomness with the requirement for equidistant point spacing, responsible for the enhanced blue noise spectral properties. We derive a highly efficient multi-scale sampling scheme for drawing random point distributions from this model. The new scheme avoids the critical slowing down phenomena that plagues this type of models. This derivation is accompanied by a model-specific analysis.

Altogether, our approach generates high-quality point distributions, supports spatially-varying spatial point density, and runs in time that is linear in the number of points generated.