Flipping geometric triangulations on hyperbolic surfaces - Archive ouverte HAL
Article Dans Une Revue Journal of Computational Geometry Année : 2024

Flipping geometric triangulations on hyperbolic surfaces

Résumé

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 prove that any Delaunay triangulation is geometric, and 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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hal-04857057 , version 1 (27-12-2024)

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Vincent Despré, Jean-Marc Schlenker, Monique Teillaud. Flipping geometric triangulations on hyperbolic surfaces. Journal of Computational Geometry, 2024, ⟨10.20382/jocg.v15i1a8⟩. ⟨hal-04857057⟩
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