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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
GRAVIR - IMAG - Laboratoire d'informatique GRAphique, VIsion et Robotique de Grenoble, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : 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.
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https://hal.inria.fr/inria-00001143
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Submitted on : Wednesday, November 9, 2016 - 2:07:25 PM
Last modification on : Friday, March 19, 2021 - 11:56:04 AM
Long-term archiving on: : Tuesday, March 14, 2017 - 11:33:25 PM

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

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