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Robust construction of the extended three-dimensional flow complex

Frédéric Cazals 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : 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.
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Submitted on : Tuesday, May 23, 2006 - 4:53:21 PM
Last modification on : Friday, February 4, 2022 - 3:18:41 AM
Long-term archiving on: : Tuesday, February 22, 2011 - 11:01:01 AM


  • HAL Id : inria-00071364, version 1



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



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