Poisson–Delaunay Mosaics of Order k

The order-k Voronoi tessellation of a locally finite set [Formula: see text] decomposes [Formula: see text] 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 f...

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Detalles Bibliográficos
Autores principales: Edelsbrunner, Herbert, Nikitenko, Anton
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2018
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6828637/
https://www.ncbi.nlm.nih.gov/pubmed/31749513
http://dx.doi.org/10.1007/s00454-018-0049-2
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author Edelsbrunner, Herbert
Nikitenko, Anton
author_facet Edelsbrunner, Herbert
Nikitenko, Anton
author_sort Edelsbrunner, Herbert
collection PubMed
description The order-k Voronoi tessellation of a locally finite set [Formula: see text] decomposes [Formula: see text] 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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spelling pubmed-68286372019-11-18 Poisson–Delaunay Mosaics of Order k Edelsbrunner, Herbert Nikitenko, Anton Discrete Comput Geom Article The order-k Voronoi tessellation of a locally finite set [Formula: see text] decomposes [Formula: see text] 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. Springer US 2018-12-04 2019 /pmc/articles/PMC6828637/ /pubmed/31749513 http://dx.doi.org/10.1007/s00454-018-0049-2 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Edelsbrunner, Herbert
Nikitenko, Anton
Poisson–Delaunay Mosaics of Order k
title Poisson–Delaunay Mosaics of Order k
title_full Poisson–Delaunay Mosaics of Order k
title_fullStr Poisson–Delaunay Mosaics of Order k
title_full_unstemmed Poisson–Delaunay Mosaics of Order k
title_short Poisson–Delaunay Mosaics of Order k
title_sort poisson–delaunay mosaics of order k
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6828637/
https://www.ncbi.nlm.nih.gov/pubmed/31749513
http://dx.doi.org/10.1007/s00454-018-0049-2
work_keys_str_mv AT edelsbrunnerherbert poissondelaunaymosaicsoforderk
AT nikitenkoanton poissondelaunaymosaicsoforderk

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