### Abstract

A simple polygon P is said to be weakly externally visible from a line segment if the line segment is outside P and if for every point x on the boundary of P there is a point y on the line segment such that the interior of the line segment xy does not intersect the interior of P. In this paper a linear time algorithm is proposed for computing the shortest line segment from which a simple polygon 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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Title of host publication | Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings |

Publisher | Springer-Verlag |

Pages | 412-424 |

Number of pages | 13 |

ISBN (Print) | 9783540475668 |

DOIs | |

State | Published - Jan 1 1991 |

Event | 2nd Workshop on Algorithms and Data Structures, WADS 1991 - Ottawa, Canada Duration: Aug 14 1991 → Aug 16 1991 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 519 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 2nd Workshop on Algorithms and Data Structures, WADS 1991 |
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Country | Canada |

City | Ottawa |

Period | 8/14/91 → 8/16/91 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings*(pp. 412-424). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 519 LNCS). Springer-Verlag. https://doi.org/10.1007/BFb0028280

**A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visible.** / Bhattacharya, Binary K.; Mukhopadhyay, Asish; Toussaint, Godfried.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 519 LNCS, Springer-Verlag, pp. 412-424, 2nd Workshop on Algorithms and Data Structures, WADS 1991, Ottawa, Canada, 8/14/91. https://doi.org/10.1007/BFb0028280

}

TY - GEN

T1 - A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visible

AU - Bhattacharya, Binary K.

AU - Mukhopadhyay, Asish

AU - Toussaint, Godfried

PY - 1991/1/1

Y1 - 1991/1/1

N2 - A simple polygon P is said to be weakly externally visible from a line segment if the line segment is outside P and if for every point x on the boundary of P there is a point y on the line segment such that the interior of the line segment xy does not intersect the interior of P. In this paper a linear time algorithm is proposed for computing the shortest line segment from which a simple polygon 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 if the line segment is outside P and if for every point x on the boundary of P there is a point y on the line segment such that the interior of the line segment xy does not intersect the interior of P. In this paper a linear time algorithm is proposed for computing the shortest line segment from which a simple polygon 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.

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U2 - 10.1007/BFb0028280

DO - 10.1007/BFb0028280

M3 - Conference contribution

SN - 9783540475668

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 412

EP - 424

BT - Algorithms and Data Structures - 2nd Workshop, WADS 1991, Proceedings

PB - Springer-Verlag

ER -