Recursive Wang Tiles for Real-Time Blue Noise

Johannes Kopf
University of Konstanz


Daniel Cohen-Or
Tel Aviv University


Oliver Deussen
University of Konstanz


Dani Lischinski
The Hebrew University

Zooming into a stippled non-photorealistic rendering. Each image shows a subset of the same implicitly infinite point set: while zooming in, more points are shown to maintain the apparent density. Only the local visible area of the point set was evaluated for each image. Interactive texture painting application. The user controls the placement of textons by directly painting individual density maps for different texton classes using various brushes. The high speed of our technique allows computing the instance positions on-the-fly from the density maps only where needed at any given time.


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 a 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.
    author  = {Johannes Kopf and Daniel Cohen-Or and Oliver Deussen
               and Dani Lischinski},
    title   = {Recursive Wang Tiles for Real-Time Blue Noise},
    journal = {ACM Transactions on Graphics (Proceedings of SIGGRAPH 2006)},
    year    = {2006},
    volume  = {25},
    number  = {3},
    pages   = {509-518},
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Source Code
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Example Tile Sets
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Stippling Demo

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Spectral Analysis
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