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

Sabrina Dammertz (), Holger Dammertz () and Alexander Keller ()
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Sabrina Dammertz: Ulm University, Institute of Media Informatics

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2008, 2009, pp 271-287 from Springer

Abstract: 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.

Keywords: Minimum Distance; Computer Graphic; Generator Vector; Lattice Basis; Graphic Application (search for similar items in EconPapers)
Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-04107-5_16

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DOI: 10.1007/978-3-642-04107-5_16

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