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.
Edelsbrunner H, Nikitenko A. Poisson-Delaunay mosaics of order k. arXiv:170909380.
Edelsbrunner, H., & Nikitenko, A. (n.d.). Poisson-Delaunay mosaics of order k. ArXiv:1709.09380.
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson-Delaunay Mosaics of Order K.” ArXiv:1709.09380, n.d.
H. Edelsbrunner and A. Nikitenko, “Poisson-Delaunay mosaics of order k,” arXiv:1709.09380. .
Edelsbrunner H, Nikitenko A. Poisson-Delaunay mosaics of order k. arXiv:1709.09380.
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson-Delaunay Mosaics of Order K.” ArXiv:1709.09380.
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