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Flipping Geometric Triangulations on Hyperbolic Surfaces

Vincent Despré 1 Jean-Marc Schlenker 2 Monique Teillaud 1
1 GAMBLE - Geometric Algorithms and Models Beyond the Linear and Euclidean realm
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
2 Mathematics Research Unit, BLG
Abstract : We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint geodesic segments. We prove that the flip graph of geometric triangulations with fixed vertices of a flat torus or a closed hyperbolic surface is connected. We give upper bounds on the number of edge flips that are necessary to transform any geometric triangulation on such a surface into a Delaunay triangulation.
Keywords : Hyperbolic surface Topology Delaunay triangulation Algorithm Flip graph Hyperbolic surf... Delaunay triang...
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https://hal.inria.fr/hal-02886493
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Vincent Despré, Jean-Marc Schlenker, Monique Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces. SoCG 2020 - 36th International Symposium on Computational Geometry, 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.35⟩. ⟨hal-02886493⟩

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