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Poisson-Delaunay Mosaics of Order k
Herbert Edelsbrunner1, Anton Nikitenko1
1IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria.
Abstract:
The order-k Voronoi tessellation of a locally finite set decomposes into convex domains whose points have the same k nearest neighbors in X. Assuming X is a stationary Poisson point process, we give explicit formulas for the expected number and total area of faces of a given dimension per unit volume of space. We also develop a relaxed version of discrete Morse theory and generalize by counting only faces, for which the k nearest points in X are within a given distance threshold.
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