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Conference Papers Year : 2012

Covering spaces and Delaunay triangulations of the 2D flat torus

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Abstract

A previous algorithm was computing the Delaunay triangulation of the flat torus, by using a 9-sheeted covering space. We propose a modification of the algorithm using only a 8-sheeted covering space, which allows to work with 8 periodic copies of the input points instead of 9. The main interest of our contribution is not only this result, but most of all the method itself: this new construction of covering spaces generalizes to Delaunay triangulations of surfaces of higher genus.

Domains

Computer Science [cs] Computational Geometry [cs.CG]
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https://hal.inria.fr/hal-01109626

Submitted on : Monday, January 26, 2015-4:15:55 PM

Last modification on : Saturday, June 25, 2022-9:09:21 PM

Long-term archiving on: Monday, April 27, 2015-10:45:57 AM

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hal-01109626 , version 1 (26-01-2015)

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  • HAL Id : hal-01109626 , version 1

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Mikhail Bogdanov, Monique Teillaud, Gert Vegter. Covering spaces and Delaunay triangulations of the 2D flat torus. 28th European Workshop on Computational Geometry, Mar 2012, Assisi, Italy. ⟨hal-01109626⟩

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