Computing a canonical polygonal schema of an orientable triangulated surface | Zendy

Francis Lazarus | Zendy; Michel Pocchiola | Zendy; Gert Vegter | Zendy; Anne Verroust-Blondet | Zendy

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Computing a canonical polygonal schema of an orientable triangulated surface

Author(s) -

Francis Lazarus,

Michel Pocchiola,

Gert Vegter,

Anne Verroust-Blondet

Publication year - 2001

Publication title -

hal (le centre pour la communication scientifique directe)

Language(s) - English

Resource type - Conference proceedings

ISBN - 1-58113-357-X

DOI - 10.1145/378583.378630

Subject(s) - polyhedron , disjoint sets , inverse , combinatorics , surface (topology) , schema (genetic algorithms) , mathematics , computer science , polygonal chain , geometry , machine learning , regular polygon

International audienceA closed orientable surface of genus g can be obtained by appropriate identi cation of pairs of edges of a 4g-gon (the polygonal schema). The identi ed edges form 2g loops on the surface, that are disjoint except for their common end-point. These loops are generators of both the fundamental group and the homology group of the surface. The inverse problem is concerned with nding a set of 2g loops on a triangulated surface, such that cutting the surface along these loops yields a (canonical) polygonal schema. We present two optimal algorithms for this inverse problem. Both algorithms have been implemented using the CGAL polyhedron data structure

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