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Sampling is fundamental to computer graphics, as samples are used both for representing data and computing averages in the process of forming images. In this context rank-1 lattices are explored with respect to image and texture representation, simulation, and image synthesis. We also contribute the necessary algorithmic and theoretical investigations to find rank-1 lattices, which are suitable for specific requirements. Opposite to common belief, it turns out that rank-1 lattices improve graphics applications quite notably and result in more efficient algorithms, too.

Rank-1 lattices in computer graphics