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Delaunay triangulations of generalized Bolza surfaces

Abstract : The Bolza surface can be seen as the quotient of the hyperbolic plane, represented by the Poincaré disk model, under the action of the group generated by the hyperbolic isometries identifying opposite sides of a regular octagon centered at the origin. We consider _generalized_ Bolza surfaces Mg, where the octagon is replaced by a regular 4g-gon, leading to a genus g surface. We propose an extension of Bowyer's algorithm to these surfaces. In particular, we compute the value of the systole of Mg. We also propose algorithms computing small sets of points on Mg that are used to initialize Bowyer's algorithm.
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https://hal.inria.fr/hal-03080125
Contributor : Monique Teillaud <>
Submitted on : Thursday, March 11, 2021 - 3:03:00 PM
Last modification on : Friday, March 12, 2021 - 3:32:23 AM

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  • HAL Id : hal-03080125, version 2
  • ARXIV : 2103.05960

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Matthijs Ebbens, Iordan Iordanov, Monique Teillaud, Gert Vegter. Delaunay triangulations of generalized Bolza surfaces. 2021. ⟨hal-03080125v2⟩

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