Computing a Dirichlet Domain for a Hyperbolic Surface
Abstract
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.
Keywords
Domains
Computational Geometry [cs.CG]
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| Origin | Files produced by the author(s) |
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| Format | Figure, Image |
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