Area Bounds of Rectilinear Polygons Realized by Angle Sequences

  • Sang Won Bae
  • Yoshio Okamoto
  • Chan-Su Shin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7676)


Given a sequence S of angles at n vertices of a rectilinear polygon, S directly defines (or realizes) a set of rectilinear polygons in the integer grid. Among such realizations, we consider the one P(S) with minimum area. Let δ(n) be the minimum of the area of P(S) over all angle sequences S of length n, and Δ(n) be the maximum. In this paper, we provide the explicit formula for δ(n) and Δ(n).


Minimum Area Simple Polygon Monotone Sequence Counterclockwise Order Extreme Edge 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Sang Won Bae
    • 1
  • Yoshio Okamoto
    • 2
  • Chan-Su Shin
    • 3
  1. 1.Dept. of Computer ScienceKyonggi UniversityKorea
  2. 2.Dept. of Communication Engineering and InformaticsUniversity of Electro-CommunicationsJapan
  3. 3.Dept. of Digital Information EngineeringHankuk University of Foreign StudiesKorea

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