# Finding an ordinary conic and an ordinary hyperplane

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : Given a finite set of non-collinear points in the plane, there exists a line that passes through exactly two points. Such a line is called an ordinary line''. An efficient algorithm for computing such a line was proposed by Mukhopadhyay et al. In this note we extend this result in two directions. We first show how to use this algorithm to compute an `ordinary conic'', that is, a conic passing through exactly five points, assuming that all the points do not lie on the same conic. Both our proofs of existence and the consequent algorithms are simpler than previous ones. We next show how to compute an ordinary hyperplane in three and higher dimensions.
Type de document :
Article dans une revue
Nordic Journal of Computing, Publishing Association Nordic Journal of Computing, 1999, 6, pp.462-468

Littérature citée [15 références]

https://hal.inria.fr/inria-00168174
Contributeur : Olivier Devillers <>
Soumis le : vendredi 24 août 2007 - 18:09:28
Dernière modification le : samedi 27 janvier 2018 - 01:31:48
Document(s) archivé(s) le : jeudi 8 avril 2010 - 21:26:41

### Fichier

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

### Identifiants

• HAL Id : inria-00168174, version 1

### Citation

Olivier Devillers, Asish Mukhopadhyay. Finding an ordinary conic and an ordinary hyperplane. Nordic Journal of Computing, Publishing Association Nordic Journal of Computing, 1999, 6, pp.462-468. 〈inria-00168174〉

### Métriques

Consultations de la notice

## 303

Téléchargements de fichiers