On the Computation of the Topology of a Non-Reduced Implicit Space Curve

Daouda Diatta 1 Bernard Mourrain 2 Olivier Ruatta 1
1 DMI
XLIM - XLIM
2 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure (PLS) isotopic to the original space curve. The algorithm is designed to provide the exact result for all inputs. It's a symbolic-numeric algorithm based on subresultant computation. Simple algebraic criteria are given to certify the output of the algorithm. The algorithm uses only one projection of the non-reduced space curve augmented with adjacency information around some "particular points" of the space curve. The algorithm is implemented with the Mathemagix Computer Algebra System (CAS) using the SYNAPS library as a backend.
Type de document :
Communication dans un congrès
J. Rafael Sendra, Loreano Gonzalez-Vega. ISSAC, Jul 2008, Linz, Austria. ACM, pp.47-54, 2008, 〈10.1145/1390768.1390778〉
Liste complète des métadonnées

Littérature citée [15 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-00218271
Contributeur : Olivier Ruatta <>
Soumis le : vendredi 7 mars 2008 - 15:14:15
Dernière modification le : jeudi 11 janvier 2018 - 16:14:45
Document(s) archivé(s) le : jeudi 29 avril 2010 - 19:49:31

Fichiers

TopologySpaceCurves.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Daouda Diatta, Bernard Mourrain, Olivier Ruatta. On the Computation of the Topology of a Non-Reduced Implicit Space Curve. J. Rafael Sendra, Loreano Gonzalez-Vega. ISSAC, Jul 2008, Linz, Austria. ACM, pp.47-54, 2008, 〈10.1145/1390768.1390778〉. 〈hal-00218271〉

Partager

Métriques

Consultations de la notice

505

Téléchargements de fichiers

246