Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere

Abstract : This paper presents a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the \sk\ is made through the calculation of the exact arrangement of circles on a sphere. On average while computing arrangements with few degeneracies (on sample molecular models), it is shown that certifying the result incurs a modest factor of two with respect to calculations using a plain double arithmetic.
Type de document :
Article dans une revue
Computational Geometry, Elsevier, 2009
Liste complète des métadonnées

Littérature citée [36 références]  Voir  Masquer  Télécharger
Contributeur : Sebastien Loriot <>
Soumis le : mardi 25 novembre 2008 - 15:17:45
Dernière modification le : vendredi 12 janvier 2018 - 01:56:01
Document(s) archivé(s) le : mardi 9 octobre 2012 - 14:42:48


Fichiers produits par l'(les) auteur(s)


  • HAL Id : inria-00335865, version 1



Pedro De Castro, Frédéric Cazals, Sebastien Loriot, Monique Teillaud. Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere. Computational Geometry, Elsevier, 2009. 〈inria-00335865〉



Consultations de la notice


Téléchargements de fichiers