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.
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Dammertz, S., Keller, A. (2008). Image Synthesis by Rank-1 Lattices. In: Keller, A., Heinrich, S., Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74496-2_12
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DOI: https://doi.org/10.1007/978-3-540-74496-2_12
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