Variable Radii Poisson Disk Sampling

We introduce three natural and well-dened generalizations of maximal Poisson-disk sampling. The rst is to decouple the disk-free (inhibition) radius from the maximality (coverage) radius. Selecting a smaller inhibition radius than the coverage radius yields samples which mix advantages of Poisson-disk and uniform-random samplings. The second generalization yields hierarchical samplings, by scaling inhibition and coverage radii by an abstract parameter, e.g. time. The third generalization is to allow the radii to vary spatially, according to a formally characterized sizing function. We state bounds on edge lengths and angles in a Delaunay triangulation of the points, dependent on the ratio of inhibition to coverage radii, or the sizing function’s Lipschitz constant. Hierarchical samplings have distributions similar to those created directly.

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