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We introduce a fast tile-based method for adaptive two-dimensional sampling with user-specified spectral properties. At the core of our approach is a deterministic, hierarchical construction of self-similar, equi-area, tri-hex tiles whose centroids have a spatial distribution free of spurious spectral peaks. A lookup table of sample points, computed offline using any existing point set optimizer to shape the samples' Fourier spectrum, is then used to populate the tiles. The result is a linear-time, adaptive, and high-quality sampling of arbitrary density functions that conforms to the desired spectral distribution, achieving a speed improvement of several orders of magnitude over current spectrum-controlled sampling methods.
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Wachtel et al. (2014) studied this question.
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