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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
Abstract : We consider geometric triangulations of surfaces, i.e., triangulations whose edges can be realized by disjoint locally 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.
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https://hal.inria.fr/hal-02400219
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Submitted on : Monday, December 9, 2019 - 2:00:23 PM
Last modification on : Friday, February 4, 2022 - 9:00:13 AM
Long-term archiving on: : Tuesday, March 10, 2020 - 5:39:08 PM

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  • HAL Id : hal-02400219, version 1
  • ARXIV : 1912.04640

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Vincent Despré, Jean-Marc Schlenker, Monique Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces. [Research Report] INRIA. 2019. ⟨hal-02400219⟩

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