AbstractGiven 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. (1997).
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.
Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling
Additional Key Words and Phrases: Computational Geometry, degenerate configurations, ordinary line, ordinary conic, ordinary hyperplane
Selected references
- Asish Mukhopadhyay, Alok Agrawal, and Ravi Mohan Hosabettu. On the Ordinary Line Problem in Computational Geometry. Nordic Journal of Computing, 4(4):330-341, Winter 1997.