Covering a Simple Polygon by Monotone Directions

  • Hee-Kap Ahn
  • Peter Brass
  • Christian Knauer
  • Hyeon-Suk Na
  • Chan-Su Shin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5369)


In this paper we study the problem of finding a set of k directions for a given simple polygon P, such that for each point p ∈ P there is at least one direction in which the line through p intersects the polygon only once. For k = 1, this is the classical problem of finding directions in which the polygon is monotone, and all such directions can be found in linear time for a simple n-gon. For k > 1, this problem becomes much harder; we give an O(n 5log2 n)-time algorithm for k = 2, and O(n 3k + 2)-time algorithm for k ≥ 3. These results are the first on the generalization of the monotonicity problem.


Convex Hull Edge Incident Simple Polygon Combinatorial Description Angle Space 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Peter Brass
    • 2
  • Christian Knauer
    • 3
  • Hyeon-Suk Na
    • 4
  • Chan-Su Shin
    • 5
  1. 1.Department of Computer Science and EngineeringPOSTECHKorea
  2. 2.Department of Computer ScienceCity CollegeNew YorkUSA
  3. 3.Institute of Computer ScienceFree University BerlinGermany
  4. 4.School of ComputingSoongsil UniversitySeoulKorea
  5. 5.School of Electrical and Information EngineeringHankuk University of Foreign StudiesKorea

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