Computational geometry: an introduction
Computational geometry: an introduction
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Simultaneous containment of several polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
On the ordinary line problem in computational geometry
Nordic Journal of Computing
Wedges in euclidean arrangements
JCDCG'04 Proceedings of the 2004 Japanese conference on Discrete and Computational Geometry
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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.[10].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.