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.
|Title of host publication||EPRINTS-BOOK-TITLE|
|Publisher||University of Groningen, Johann Bernoulli Institute for Mathematics and Computer Science|
|Number of pages||10|
|Publication status||Published - 2001|