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Efficient Search for Two-Dimensional Rank-1 Lattices with Applications in Graphics

In: Monte Carlo and Quasi-Monte Carlo Methods 2008

Author

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  • Sabrina Dammertz

    (Ulm University, Institute of Media Informatics)

  • Holger Dammertz

  • Alexander Keller

Abstract

Selecting rank-1 lattices with respect to maximized mutual minimum distance has been shown to be very useful for image representation and synthesis in computer graphics. While algorithms using rank-1 lattices are very simple and efficient, the selection of their generator vectors often has to resort to exhaustive computer searches, which is prohibitively slow. For the two-dimensional setting, we introduce an efficient approximate search algorithm and transfer the principle to the search for maximum minimum distance rank-1 lattice sequences. We then extend the search for rank-1 lattices to approximate a given spectrum and present new algorithms for anti-aliasing and texture representation in computer graphics.

Suggested Citation

  • Sabrina Dammertz & Holger Dammertz & Alexander Keller, 2009. "Efficient Search for Two-Dimensional Rank-1 Lattices with Applications in Graphics," Springer Books, in: Pierre L' Ecuyer & Art B. Owen (ed.), Monte Carlo and Quasi-Monte Carlo Methods 2008, pages 271-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-04107-5_16
    DOI: 10.1007/978-3-642-04107-5_16
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