Visual Computing

University of Konstanz
ACM Transactions on Graphics

Recursive Wang Tiles for Real-time Blue Noise

J. Kopf, D. Cohen-Or, O. Deussen, D. Lischinski
Teaser of Recursive Wang Tiles for Real-time Blue Noise


Paper (.pdf, 31.0 MB)


Well distributed point sets play an important role in a variety of computer graphics contexts, such as anti-aliasing, global illumination, halftoning, non-photorealistic rendering, point-based modeling and rendering, and geometry processing. In this paper, we introduce a novel technique for rapidly generating large point sets possessing a blue noise Fourier spectrum and high visual quality. Our technique generates non-periodic point sets, distributed over arbitrarily large areas. The local density of a point set may be prescribed by an arbitrary target density function, without any preset bound on the maximum density. Our technique is deterministic and tile-based; thus, any local portion of a potentially infinite point set may be consistently regenerated as needed. The memory footprint of the technique is constant, and the cost to generate any local portion of the point set is proportional to the integral over the target density in that area. These properties make our technique highly suitable for a variety of real-time interactive applications, some of which are demonstrated in the paper. Our technique utilizes a set of carefully constructed progressive and recursive blue noise Wang tiles. The use of Wang tiles enables the generation of infinite non-periodic tilings. The progressive point sets inside each tile are able to produce spatially varying point densities. Recursion allows our technique to adaptively subdivide tiles only where high density is required, and makes it possible to zoom into point sets by an arbitrary amount, while maintaining a constant apparent density.


  acmid      = {1141916},
  address    = {New York, NY, USA},
  author     = {J. Kopf and D. Cohen-Or and O. Deussen and D. Lischinski},
  doi        = {10.1145/1141911.1141916},
  issn       = {0730-0301},
  issue_date = {July 2006},
  journal    = {ACM Transactions on Graphics},
  keywords   = {Poisson disk distribution, Wang tiles, anti-aliasing, blue noise, non-periodic tiling, object positioning, sampling, stippling, texture synthesis},
  month      = {jul},
  number     = {3},
  numpages   = {10},
  pages      = {509--518},
  publisher  = {ACM},
  title      = {Recursive Wang Tiles for Real-time Blue Noise},
  url        = {},
  volume     = {25},
  year       = {2006},