School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Document Type
Article
Publication Date
7-2024
Abstract
For a locally finite set in R 2 , the order-k Brillouin tessellations form an infinite sequence of convex face-to-face tilings of the plane. If the set is coarsely dense and generic, then the corresponding infinite sequences of minimum and maximum angles are both monotonic in k. As an example, a stationary Poisson point process in R 2 is locally finite, coarsely dense, and generic with probability one. For such a set, the distributions of angles in the Voronoi tessellations, Delaunay mosaics, and Brillouin tessellations are independent of the order and can be derived from the formula for angles in order-1 Delaunay mosaics given by Miles (Math. Biosci. 6, 85–127 (1970)).
Recommended Citation
Edelsbrunner, Herbert, Alexey Garber, Mohadese Ghafari, Teresa Heiss, and Morteza Saghafian. "On angles in higher order brillouin tessellations and related tilings in the plane." Discrete & Computational Geometry 72, no. 1 (2024): 29-48. https://doi.org/10.1007/s00454-023-00566-1
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Discrete & Computational Geometry
DOI
10.1007/s00454-023-00566-1
Comments
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