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 - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
2 LIS - Laboratoire des images et des signaux
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.
Keywords : Triangulated surfaces quadrangulation surface generators Reeb graph Dijkstra's algorithm
Type de document :
Article dans une revue
Graphical Models, Elsevier, 2003, Special issue: Discrete Topology and Geometry for Image and Object Representation, 65 (1-3), pp.131-148
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generators.png
generators.png
https://hal.inria.fr/inria-00001143
Contributeur : Franck Hétroy-Wheeler <>
Soumis le : mercredi 9 novembre 2016 - 14:07:25
Dernière modification le : vendredi 14 septembre 2018 - 16:09:15
Document(s) archivé(s) le : mardi 14 mars 2017 - 23:33:25

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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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