Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2022

Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces

Abstract

Guided by insights on the mapping class group of a surface, we give experimental evidence that the upper bound recently proven on the diameter of the flip graph of a surface by Despré, Schlenker, and Teillaud (SoCG'20) is largely overestimated. To obtain this result, we propose a set of techniques allowing us to actually perform experiments. We solve arithmetic issues by proving a density result on rationally described genus two hyperbolic surfaces, and we rely on a description of surfaces allowing us to propose a data structure on which flips can be efficiently implemented.
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Dates and versions

hal-03462834 , version 1 (02-12-2021)
hal-03462834 , version 2 (11-05-2022)

Identifiers

  • HAL Id : hal-03462834 , version 2

Cite

Vincent Despré, Loïc Dubois, Benedikt Kolbe, Monique Teillaud. Experimental analysis of Delaunay flip algorithms on genus two hyperbolic surfaces. 2022. ⟨hal-03462834v2⟩
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