Discrete & Computational Geometry

, Volume 5, Issue 3, pp 289–304

# 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
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 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