Computing a Canonical Polygonal Schema of an Orientable Triangulated Surface

Francis Lazarus, Michel Pocchiola, Gert Vegter, Anne Verroust

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

76 Citations (Scopus)
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Abstract

A closed orientable surface of genus g can be obtained by appropriate identification of pairs of edges of a 4g-gon (the polygonal schema). The identified 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 finding 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.
Original languageEnglish
Title of host publicationEPRINTS-BOOK-TITLE
PublisherUniversity of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science
Number of pages10
Publication statusPublished - 2001

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