A step in the Delaunay mosaic of order k
Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15.
Download
Journal Article
| Published
| English
Scopus indexed
Department
Abstract
Given a locally finite set πββπ and an integer πβ₯0, we consider the function π°π:Delπ(π)ββ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551β559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76β83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90β145, 1998) and Freij (Discrete Math 309:3821β3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.
Publishing Year
Date Published
2021-04-01
Journal Title
Journal of Geometry
Publisher
Springer Nature
Volume
112
Issue
1
Article Number
15
ISSN
eISSN
IST-REx-ID
Cite this
Edelsbrunner H, Nikitenko A, Osang GF. A step in the Delaunay mosaic of order k. Journal of Geometry. 2021;112(1). doi:10.1007/s00022-021-00577-4
Edelsbrunner, H., Nikitenko, A., & Osang, G. F. (2021). A step in the Delaunay mosaic of order k. Journal of Geometry. Springer Nature. https://doi.org/10.1007/s00022-021-00577-4
Edelsbrunner, Herbert, Anton Nikitenko, and Georg F Osang. βA Step in the Delaunay Mosaic of Order K.β Journal of Geometry. Springer Nature, 2021. https://doi.org/10.1007/s00022-021-00577-4.
H. Edelsbrunner, A. Nikitenko, and G. F. Osang, βA step in the Delaunay mosaic of order k,β Journal of Geometry, vol. 112, no. 1. Springer Nature, 2021.
Edelsbrunner H, Nikitenko A, Osang GF. 2021. A step in the Delaunay mosaic of order k. Journal of Geometry. 112(1), 15.
Edelsbrunner, Herbert, et al. βA Step in the Delaunay Mosaic of Order K.β Journal of Geometry, vol. 112, no. 1, 15, Springer Nature, 2021, doi:10.1007/s00022-021-00577-4.
All files available under the following license(s):
Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):
Main File(s)
File Name
2021_Geometry_Edelsbrunner.pdf
694.71 KB
Access Level
Open Access
Date Uploaded
2021-06-11
MD5 Checksum
e52a832f1def52a2b23d21bcc09e646f