The order-k Voronoi tessellation of a locally finite set X⊆ Rn decomposes Rn 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.
CITATION STYLE
Edelsbrunner, H., & Nikitenko, A. (2019). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry, 62(4), 865–878. https://doi.org/10.1007/s00454-018-0049-2
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