Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph

Franck Hétroy (1) , Dominique Attali (2)

1 EVASION - Virtual environments for animation and image synthesis of natural objects
2 LIS - Laboratoire des images et des signaux

Although surfaces are more and more often represented by dense triangulations, it can be useful to convert them to B-spline surface patches, lying on quadrangles. This paper presents a method for the construction of coarse topological quadrangulations of closed triangulated surfaces, based on Morse theory. In order to construct on the surface a quadrangulation of its canonical polygonal schema, we compute first a Reeb graph then a canonical set of generators embedded on the surface. Some results are shown on different surfaces.

Mots clés: Triangulated surfaces; quadrangulation; surface generators; Reeb graph; Dijkstra's algorithm

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Géométrie algorithmique [cs.CG]

Franck Hétroy, Dominique Attali. Topological Quadrangulations of Closed Triangulated Surfaces using the Reeb Graph. Graphical Models, 2003, Special issue: Discrete Topology and Geometry for Image and Object Representation, 65 (1-3), pp.131-148. ⟨inria-00001143⟩