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On angles in higher order brillouin tessellations and related tilings in the plane. 2

Edelsbrunner, H ; Sharif University of Technology | 2024

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  1. Type of Document: Article
  2. DOI: 10.1007/s00454-023-00566-1
  3. Publisher: 2024
  4. Abstract:
  5. For a locally finite set in R2, 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 R2 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)). © The Author(s) 2023
  6. Keywords:
  7. Angles ; Computational experiments ; Delaunay and Iglesias mosaics ; Higher order ; Orthogonal dual ; Poisson point processes ; Voronoi and Brillouin tessellations
  8. Source: Discrete and Computational Geometry ; Volume 72, Issue 1 , 2024 , Pages 29-48 ; 01795376 (ISSN)
  9. URL: https://link.springer.com/article/10.1007/s00454-023-00566-1