Loops and canonical polygonal schema

(Anne Verroust-Blondet)

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 Description 

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. We propose a method to model and control topological changes by a smooth deformation of a polyhedral mesh using curves and loops. As changing the genus of a surface is not a continuous transformation,the topological change is made when an intermediate shape between the two topologies has been obtained. The creation and the deletion ofholes are studied. The deletion of a hole uses non null-homotopic loops to designate the hole to be deleted. A method computing two independent loops associated to a hole is presented.
 
 

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Email : Anne.Verroust(@)inria.fr

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