### 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 - Feb 1999 |

### 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

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## Cite this

Bhattacharya, B. K., Mukhopadhyay, A., & Toussaint, G. T. (1999). Computing a shortest weakly externally visible line segment for a simple polygon.

*International Journal of Computational Geometry and Applications*,*9*(1), 81-96. https://doi.org/10.1142/S0218195999000078