Discrete & Computational Geometry

, Volume 5, Issue 3, pp 289–304 | Cite as

Computing simple circuits from a set of line segments

  • David Rappaport
  • Hiroshi Imai
  • Godfried T. Toussaint
Article

Abstract

We address the problem of connecting line segments to form the boundary of a simple polygon—a simple circuit. However, not every set of segments can be so connected. We present anO(n logn)-time algorithm to determine whether a set of segments, constrained so that each segment has at least one endpoint on the boundary of the convex hull of the segments, admits a simple circuit. Furthermore, this technique can also be used to compute a simple circuit of minimum perimeter, or a simple circuit that bounds the minimum area, with no increase in computational complexity.

Keywords

Line Segment Convex Hull Discrete Comput Geom Weighted Graph Simple Polygon 

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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • David Rappaport
    • 1
  • Hiroshi Imai
    • 2
  • Godfried T. Toussaint
    • 3
  1. 1.Department of Computing and Information ScienceQueen's UniversityKingstonCanada
  2. 2.Department of Computer Science and Communication Engineering, Faculty of EngineeringKyushu UniversityHakozaki, FukuokaJapan
  3. 3.School of Computer ScienceMcGill UniversityMontrealCanada

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