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.
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Dammertz, S., Dammertz, H., Keller, A. (2009). Efficient Search for Two-Dimensional Rank-1 Lattices with Applications in Graphics. In: L' Ecuyer, P., Owen, A. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2008. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04107-5_16
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DOI: https://doi.org/10.1007/978-3-642-04107-5_16
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