On Tangents to Quadric Surfaces

Ciprian Borcea 1 Xavier Goaoc 2 Sylvain Lazard 2 Sylvain Petitjean 2
2 VEGAS - Effective Geometric Algorithms for Surfaces and Visibility
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : We study the variety of common tangents for up to four quadric surfaces in projective three-space, with particular regard to congurations of four quadrics admitting a continuum of common tangents. We formulate geometrical conditions in the projective space dened by all complex quadric surfaces which express the fact that several quadrics are tangent along a curve to one and the same quadric of rank at least three, and called, for intuitive reasons: a basket. Lines in any ruling of the latter will be common tangents. These considerations are then restricted to spheres in Euclidean threespace, and result in a complete answer to the question over the reals: "When do four spheres allow infinitely many common tangents?".
Type de document :
Autre publication
Manuscript. 2004
Liste complète des métadonnées

Littérature citée [13 références]  Voir  Masquer  Télécharger

https://hal.inria.fr/inria-00431701
Contributeur : Xavier Goaoc <>
Soumis le : jeudi 12 novembre 2009 - 19:56:38
Dernière modification le : jeudi 11 janvier 2018 - 06:20:14
Document(s) archivé(s) le : jeudi 17 juin 2010 - 18:02:07

Fichier

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

Identifiants

  • HAL Id : inria-00431701, version 1

Collections

Citation

Ciprian Borcea, Xavier Goaoc, Sylvain Lazard, Sylvain Petitjean. On Tangents to Quadric Surfaces. Manuscript. 2004. 〈inria-00431701〉

Partager

Métriques

Consultations de la notice

263

Téléchargements de fichiers

463