Computing a Dirichlet Domain for a Hyperbolic Surface
Résumé
This paper exhibits and analyzes an algorithm that takes a given closed orientable hyperbolic surface and outputs an explicit Dirichlet domain. The input is a fundamental polygon with side pairings. While grounded in topological considerations, the algorithm makes key use of the geometry of the surface. We introduce data structures that reflect this interplay between geometry and topology and show that the algorithm runs in polynomial time, in terms of the initial perimeter and the genus of the surface.
Mots clés
Domaines
Géométrie algorithmique [cs.CG]
Fichier principal
LIPIcs-SoCG-2023-27.pdf (1.22 Mo)
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| Origine | Fichiers produits par l'(les) auteur(s) |
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| Format | Figure, Image |
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