# 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.
Document type :
Journal articles

Cited literature [15 references]

https://hal.inria.fr/inria-00168174
Contributor : Olivier Devillers <>
Submitted on : Friday, August 24, 2007 - 6:09:28 PM
Last modification on : Friday, April 24, 2020 - 2:08:04 PM
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• 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⟩

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