### Abstract

A simple polygon P is said to be weakly externally visible from a line segment L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of pq lies inside P. In this paper, a linear time algorithm is proposed for computing a shortest line segment from which P is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.

Original language | English (US) |
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Pages (from-to) | 81-96 |

Number of pages | 16 |

Journal | International Journal of Computational Geometry and Applications |

Volume | 9 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1999 |

### Fingerprint

### Keywords

- External visibility
- Polygon
- Shortest visible line segment
- Weak visibility

### ASJC Scopus subject areas

- Theoretical Computer Science
- Geometry and Topology
- Computational Theory and Mathematics
- Computational Mathematics
- Applied Mathematics

### Cite this

*International Journal of Computational Geometry and Applications*,

*9*(1), 81-96. https://doi.org/10.1142/S0218195999000078

**Computing a shortest weakly externally visible line segment for a simple polygon.** / Bhattacharya, Binay K.; Mukhopadhyay, Asish; Toussaint, Godfried.

Research output: Contribution to journal › Article

*International Journal of Computational Geometry and Applications*, vol. 9, no. 1, pp. 81-96. https://doi.org/10.1142/S0218195999000078

}

TY - JOUR

T1 - Computing a shortest weakly externally visible line segment for a simple polygon

AU - Bhattacharya, Binay K.

AU - Mukhopadhyay, Asish

AU - Toussaint, Godfried

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A simple polygon P is said to be weakly externally visible from a line segment L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of pq lies inside P. In this paper, a linear time algorithm is proposed for computing a shortest line segment from which P is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.

AB - A simple polygon P is said to be weakly externally visible from a line segment L if it lies outside P and for every point p on the boundary of P there is a point q on L such that no point in the interior of pq lies inside P. In this paper, a linear time algorithm is proposed for computing a shortest line segment from which P is weakly externally visible. This is done by a suitable generalization of a linear time algorithm which solves the same problem for a convex polygon.

KW - External visibility

KW - Polygon

KW - Shortest visible line segment

KW - Weak visibility

UR - http://www.scopus.com/inward/record.url?scp=0033484876&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033484876&partnerID=8YFLogxK

U2 - 10.1142/S0218195999000078

DO - 10.1142/S0218195999000078

M3 - Article

AN - SCOPUS:0033484876

VL - 9

SP - 81

EP - 96

JO - International Journal of Computational Geometry and Applications

JF - International Journal of Computational Geometry and Applications

SN - 0218-1959

IS - 1

ER -