Computing a Canonical Polygonal Schema of an Orientable Triangulated Surface

Francis Lazarus (1) , Michel Pocchiola (2) , Gert Vegter (3) , Anne Verroust (4)

1 SIC - SIGNAL-IMAGE-COMMUNICATION
2 LIENS - Laboratoire d'informatique de l'école normale supérieure
3 Bernoulli Institute for Mathematics and Computer Science and Artificial Intelligence
4 INRIA Rocquencourt

A 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.

Domaines: Géométrie algorithmique [cs.CG]

Francis Lazarus, Michel Pocchiola, Gert Vegter, Anne Verroust. Computing a Canonical Polygonal Schema of an Orientable Triangulated Surface. SoCG '01 - Seventeenth annual symposium on Computational geometry, Jun 2001, Medford, United States. pp.80-89, ⟨10.1145/378583.378630⟩. ⟨hal-00804691⟩