Finding an Ordinary Conic and an Ordinary Hyperplane

Olivier Devillers 1 Asish Mukhopadhyay
1 PRISME - Geometry, Algorithms and Robotics
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 {\em 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 {\em ordinary conic}, that is, a conic passing through exactly five points, assuming that all the points do not lie onthe same conic. Our proof of existence and the consequent algorithm is simpler than previous ones. We also show how to compute an ordinary hyperplane in threeand higher dimensions.
Type de document :
Rapport
RR-3517, INRIA. 1998
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https://hal.inria.fr/inria-00073167
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Soumis le : mercredi 24 mai 2006 - 12:02:18
Dernière modification le : jeudi 11 janvier 2018 - 16:40:44
Document(s) archivé(s) le : dimanche 4 avril 2010 - 23:36:41

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Olivier Devillers, Asish Mukhopadhyay. Finding an Ordinary Conic and an Ordinary Hyperplane. RR-3517, INRIA. 1998. 〈inria-00073167〉

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