Poisson–Delaunay Mosaics of Order k

H. Edelsbrunner, A. Nikitenko, Discrete and Computational Geometry 62 (2019) 865–878.

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Journal Article | Published | 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.
Publishing Year
Date Published
2019-12-01
Journal Title
Discrete and Computational Geometry
Volume
62
Issue
4
Page
865–878
ISSN
eISSN
IST-REx-ID

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Edelsbrunner H, Nikitenko A. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 2019;62(4):865–878. doi:10.1007/s00454-018-0049-2
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
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry 62, no. 4 (2019): 865–878. https://doi.org/10.1007/s00454-018-0049-2.
H. Edelsbrunner and A. Nikitenko, “Poisson–Delaunay Mosaics of Order k,” Discrete and Computational Geometry, vol. 62, no. 4, pp. 865–878, 2019.
Edelsbrunner H, Nikitenko A. 2019. Poisson–Delaunay Mosaics of Order k. Discrete and Computational Geometry. 62(4), 865–878.
Edelsbrunner, Herbert, and Anton Nikitenko. “Poisson–Delaunay Mosaics of Order K.” Discrete and Computational Geometry, vol. 62, no. 4, Springer, 2019, pp. 865–878, doi:10.1007/s00454-018-0049-2.
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