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Flipping Geometric Triangulations on Hyperbolic Surfaces


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.
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Dates and versions

hal-02886493 , version 1 (01-07-2020)



Vincent Despré, Jean-Marc Schlenker, Monique Teillaud. Flipping Geometric Triangulations on Hyperbolic Surfaces. SoCG 2020 - 36th International Symposium on Computational Geometry, Jun 2020, Zurich, Switzerland. ⟨10.4230/LIPIcs.SoCG.2020.35⟩. ⟨hal-02886493⟩
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