HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation

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.
Document type :
Complete list of metadata

Contributor : Rapport de Recherche Inria Connect in order to contact the contributor
Submitted on : Wednesday, May 24, 2006 - 12:02:18 PM
Last modification on : Friday, February 4, 2022 - 3:14:49 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:36:41 PM


  • HAL Id : inria-00073167, version 1



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



Record views


Files downloads