Transversal of disjoint convex polygons

  • Authors:

  • Francis Y. L. Chin;Hong Shen;Fu Lee Wang

  • Affiliations:

  • Department of Computer Science and Information Systems, The University of Hong Kong, Pokfulam Road, Hong Kong;Graduate School of Information Science, Japan Advanced Institute of Science & Technology, Tatsunokuchi, Ishikawa 923-1292, Japan;Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, Hong Kong

  • Venue:
  • Information Processing Letters
  • Year:
  • 2003

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Abstract

Given a set S of n disjoint convex polygons {Pi | 1 ≤ i ≤ n} in a plane, each with ki vertices, the transversal problem is to find, if there exists one, a straight line that goes through every polygon in S. We show that the transversal problem can be solved in O(N + n log n) time, where N = Σi=1n ki is the total number of vertices of the polygons.