AA Patterns for Point Sets with Controlled Spectral Properties

ACM Transactions on Graphics
(Proceedings of SIGGRAPH ASIA 2015)

Abdalla G. M. Ahmed1     Hui Huang2     Oliver Deussen1;2

1University of Konstanz, Germany      2Shenzhen VisuCA Key Lab / SIAT, China

Figure 1: AA(183/112); morphed as (left-to-right): BNOT blue noise profile, FPO-like profile, step blue noise, green noise, and pink noise.


We describe a novel technique for the fast production of large point sets with different spectral properties. In contrast to tile-based methods we use so-called AA Patterns: ornamental point sets obtained from quantization errors. These patterns have a discrete and structured number-theoretic nature, can be produced at very low cost, and possess an inherent structural indexing mechanism equivalent to those used in recursive tiling techniques. This allows us to generate, manipulate and store point sets very efficiently. The technique outperforms existing methods in speed, memory footprint, quality, and flexibility. This is demonstrated by a number of measurements and comparisons to existing point generation algorithms.

Codes and data:  download from below.
[To reference our code or data in a publication, please include the bibtex below and a link to this website.] 


We thank the anonymous reviewers for their great help in shaping this paper. Thanks to Mohamed Sayed for his discussions during an early stage of the idea. This work was supported in part by the Deutsche Forschungsgemeinschaft Grant DE-620/22-1, Foreign 1000 Talent Plan (WQ201344000169), NSFC (61522213, 61379090), 973 Program (2014CB360503), Guangdong Science and Technology Program (2015A030312015, 2014B050502009), Shenzhen VisuCA Key Lab (CXB201104220029A).


@ ARTICLE {ahmed2015aa,
  title={AA patterns for point sets with controlled spectral properties},
  author={Ahmed, Abdalla GM and Huang, Hui and Deussen, Oliver},
  journal={ACM Transactions on Graphics (TOG)},

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