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[KCD+06]  Recursive Wang Tiles for Real-Time Blue Noise

Kopf:2006:RWT (Article)
Author(s)Kopf J., Cohen-Or D., Deussen O. and Lischinski D.
Title« Recursive Wang Tiles for Real-Time Blue Noise »
JournalACM Transactions on Graphics, Proceedings of ACM SIGGRAPH 2006 (Boston, MA, July 30--August 3, 2006)
Volume25
Number3
Page(s)509--518
Year2006
URLhttp://graphics.uni-konstanz.de/publications/2006/blue_noise/

Abstract
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.

BibTeX code
@article{Kopf:2006:RWT,
  optpostscript = {},
  number = {3},
  month = jul,
  author = {Johannes Kopf and Daniel Cohen-Or and Oliver Deussen and Dani
            Lischinski},
  optkey = {},
  optannote = {},
  url = {http://graphics.uni-konstanz.de/publications/2006/blue_noise/},
  localfile = {papers/Kopf.2006.RWT.pdf},
  optkeywords = {},
  doi = {http://doi.acm.org/10.1145/1141911.1141916},
  optciteseer = {},
  journal = SIGGRAPH2006,
  volume = {25},
  optwww = {},
  title = {{R}ecursive {W}ang {T}iles for {R}eal-{T}ime {B}lue {N}oise},
  abstract = {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.},
  pages = {509--518},
  year = {2006},
}

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