On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane

Authors

Herbert Edelsbrunner
Alexey Garber, The University of Texas Rio Grande Valley
Mohadese Ghafari
Teresa Heiss
Morteza Saghafian

Document Type

Article

Publication Date

9-7-2023

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)).

Comments

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Recommended Citation

Edelsbrunner, H., Garber, A., Ghafari, M. et al. On Angles in Higher Order Brillouin Tessellations and Related Tilings in the Plane. Discrete Comput Geom (2023). 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 Comput Geom

DOI

10.1007/s00454-023-00566-1