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# Finding an Ordinary Conic and an Ordinary Hyperplane

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.
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https://hal.inria.fr/inria-00073167
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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

### Identifiers

• HAL Id : inria-00073167, version 1

### Citation

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

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