Robust construction of the extended three-dimensional flow complex - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Rapport (Rapport De Recherche) Année : 2006

Robust construction of the extended three-dimensional flow complex

Frédéric Cazals

Résumé

The Delaunay triangulation and its dual the Voronoi diagram are ubiquitous geometric complexes. From a topological standpoint, the connexion has recently been made between these constructions and the Morse theory of distance functions. In particular, algorithms have been designed to compute the flow complex induced by the distance functions to a point set. This paper develops the first complete and robust construction of the extended flow complex, which in addition of the stable manifolds of the flow complex, also features the unstable manifolds. A first difficulty comes from the interplay between the degenerate cases of Delaunay and those which are flow specific. A second class of problems comes from cascaded constructions and predicates - as opposed to the standard in-circle and orientation predicates for Delaunay. We deal with both aspects and show how to implement a complete and robust flow operator, from which the extended flow complex is easily computed. We also present experimental results.
Fichier principal
Vignette du fichier
RR-5903.pdf (858.78 Ko) Télécharger le fichier

Dates et versions

inria-00071364 , version 1 (23-05-2006)

Identifiants

  • HAL Id : inria-00071364 , version 1

Citer

Frédéric Cazals. Robust construction of the extended three-dimensional flow complex. [Research Report] RR-5903, INRIA. 2006. ⟨inria-00071364⟩
103 Consultations
53 Téléchargements

Partager

Gmail Facebook X LinkedIn More