Calcul effectif de la topologie de courbes et surfaces algébriques réelles

Daouda Diatta 1, 2
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
2 DMI
XLIM - XLIM
Abstract : In this thesis, we got interested into the Effective Computation of the Topology of Real Algebraic Curves and Surfaces. One can distinguish three main new algorithms in the field of shape representation. Our first algorithm is a certified symbolic-numerical based on sub-resultants properties and computes the topology of a plane algebraic curve with the best known complexity. The second algorithms computes the topology of a space curve defined as the intersection of two implicit algebraic surfaces. For the designing of this algorithm, we introduce the notion of space curve in pseudo-generic position with respect to a given plane. This approach leads to a certified symbolic-numerical algorithm with the best known complexity. The third algorithms is a new and complete one for computing the isotopic meshing of an implicit algebraic surface. It involves only subresultant computations and entirely relies on rational manipulation, which makes it direct to implement. Finally, we also design an algorithm for computing the cells in an arrangement of quadrics which may be classify on the area of configuration spaces computation.
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Contributor : Daouda Niang Diatta <>
Submitted on : Friday, December 4, 2009 - 5:14:22 PM
Last modification on : Thursday, January 11, 2018 - 4:04:53 PM
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Daouda Diatta. Calcul effectif de la topologie de courbes et surfaces algébriques réelles. Mathématiques [math]. Université de Limoges, 2009. Français. ⟨tel-00438817⟩

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