Poisson–Delaunay Mosaics of Order k

H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry (2018).

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Journal Article | Epub ahead of print | English
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Abstract
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.
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2018-12-04
Journal Title
Discrete and Computational Geometry
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Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2018. doi:10.1007/s00454-018-0049-2
Edelsbrunner, H., & Nikitenko, A. (2018). Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. https://doi.org/10.1007/s00454-018-0049-2
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, 2018. https://doi.org/10.1007/s00454-018-0049-2.
H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, 2018.
Edelsbrunner H, Nikitenko A. 2018. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry.
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, Springer, 2018, doi:10.1007/s00454-018-0049-2.
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