Image Synthesis by Rank-1 Lattices

Sabrina Dammertz () and Alexander Keller ()
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Sabrina Dammertz: Ulm University
Alexander Keller: Ulm University

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2006, 2008, pp 217-236 from Springer

Abstract: Summary Considering uniform points for sampling, rank-1 lattices provide the simplest generation algorithm. Compared to classical tensor product lattices or random samples, their geometry allows for a higher sampling efficiency. These considerations result in a proof that for periodic Lipschitz continuous functions, rank-1 lattices with maximized minimum distance perform best. This result is then investigated in the context of image synthesis, where we study anti-aliasing by rank-1 lattices and using the geometry of rank-1 lattices for sensor and display layouts.

Keywords: Minimum Distance; Computer Graphic; Voronoi Diagram; Voronoi Cell; Short Vector (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-74496-2_12

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DOI: 10.1007/978-3-540-74496-2_12

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