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

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 e cient, 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 e cient 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.