ACM Siggraph Asia, 2015, Proceedings

AA Patterns for Point Sets with Controlled Spectral Properties

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


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



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



Abstract

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 costs, 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.


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Bibtex

@article{Ahmed:2015:APP:2816795.2818139,
    author = {Ahmed, Abdalla G. M. and Huang, Hui and Deussen, Oliver},
    title = {AA Patterns for Point Sets with Controlled Spectral Properties},
    journal = {ACM Trans. Graph.},
    issue_date = {November 2015},
    volume = {34},
    number = {6},
    month = oct,
    year = {2015},
    issn = {0730-0301},
    pages = {212:1--212:8},
    articleno = {212},
    numpages = {8},
    url = {http://doi.acm.org/10.1145/2816795.2818139},
    doi = {10.1145/2816795.2818139},
    acmid = {2818139},
    publisher = {ACM},
    address = {New York, NY, USA},
    keywords = {blue noise, sampling methods, spectral analysis, tiling},
}

Acknowledgments

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), and Shenzhen VisuCA Key Lab (CXB201104220029A).