Blue Noise as a Lattice Gibbs Ensemble

Abstract

We present an algorithm for generating blue-noise point sets that is simultaneously local and parallel, and whose output is a draw, up to a bounded error, from an explicit probability distribution. Methods that optimize point positions achieve high spectral quality but tend to couple all points globally, while tile-based methods, the main existing local approach, assemble their output from point sets constructed offline rather than generating it from scratch; we show that locality does not require giving that up. Concretely, we model blue noise as a Gibbs distribution over a lattice, with a pairwise penalty whose continuous parameters control repulsion strength, scale, and hardness. To sample this distribution locally, we trace each site's dependencies backward in time and truncate the trace to a bounded region known before sampling begins; tiles can therefore be generated independently in any order, with no communication between them. We stipple a 14557$\times$8418 James Webb Space Telescope image tile by tile, with peak memory under 51 MiB, set by the working window rather than the image dimensions. Spectral quality is competitive with existing methods at matched density, and the construction extends naturally to multi-class outputs.

arXiv comment17 pages, 15 figures