### 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 an O(n log n)-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.

Original language | English (US) |
---|---|

Pages (from-to) | 289-304 |

Number of pages | 16 |

Journal | Discrete & Computational Geometry |

Volume | 5 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1 1990 |

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### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Cite this

*Discrete & Computational Geometry*,

*5*(1), 289-304. https://doi.org/10.1007/BF02187791

**Computing simple circuits from a set of line segments.** / Rappaport, David; Imai, Hiroshi; Toussaint, Godfried.

Research output: Contribution to journal › Article

*Discrete & Computational Geometry*, vol. 5, no. 1, pp. 289-304. https://doi.org/10.1007/BF02187791

}

TY - JOUR

T1 - Computing simple circuits from a set of line segments

AU - Rappaport, David

AU - Imai, Hiroshi

AU - Toussaint, Godfried

PY - 1990/12/1

Y1 - 1990/12/1

N2 - 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 an O(n log n)-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.

AB - 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 an O(n log n)-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.

UR - http://www.scopus.com/inward/record.url?scp=0039746344&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039746344&partnerID=8YFLogxK

U2 - 10.1007/BF02187791

DO - 10.1007/BF02187791

M3 - Article

VL - 5

SP - 289

EP - 304

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 1

ER -