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Sampling with polyominoes

We present a new general-purpose method for fast hierarchical importance sampling with blue-noise properties. Our approach is based on self-similar tiling of the plane or the surface of a sphere with rectifiable polyominoes. Sampling points are associated with polyominoes, one point per polyomino. Each polyomino is recursively subdivided until the desired local density of samples is reached. A numerical code generated during the subdivision process is used for thresholding to accept or reject the sample. The exact position of the sampling point within the polyomino is determined according to a structural index, which indicates the polyomino's local neighborhood. The variety of structural indices and associated sampling point positions are computed during the offline optimization process, and tabulated. Consequently, the sampling itself is extremely fast. The method allows both deterministic and pseudo-non-deterministic sampling. It can be successfully applied in a large variety of graphical applications, where fast sampling with good spectral and visual properties is required. The prime application is rendering.