On the ordinary line problem in computational geometry

Authors:
Asish Mukhopadhyay;Alok Agrawal;Ravi Mohan Hosabettu
Affiliations:
Department of Computer Science and Engineering, Indian Institute of Technology, Kanpur, INDIA;Oracle Corporation;CS Dept., Utah University
Venue:
Nordic Journal of Computing
Year:
1997

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Abstract

Let P be a set of n points in the plane. A connecting line of P is a line that passes through at least two of its points. A connecting line is called ordinary if it is incident on exactly two points of P. If the points of P are not collinear then such a line exists. In fact, there are Ω(n) such lines. In this paper, we present two O(n log n) time algorithms for finding an ordinary line, assuming that the points of P are not collinear. We also present an optimal O(n2) time algorithm for finding all such ordinary lines.