### Abstract

The link center of a simple polygon P is the set of points x inside P at which the maximal link-distancefrom x to any other point in P is minimized, where the link distance between two points x, y inside P isdefined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We proveseveral geometric properties of the link center and present an algorithm that calculates this set in time0(n^{2}), where n is the number of sides of P. We also give an 0 (n log n) algorithm for finding apoint x in an approximate link center, namely the maximal link distance from x to any point in P is at most one more than the value attained from the link center.

Original language | English (US) |
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Title of host publication | Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987 |

Publisher | Association for Computing Machinery, Inc |

Pages | 1-10 |

Number of pages | 10 |

ISBN (Electronic) | 0897912314, 9780897912310 |

DOIs | |

State | Published - Oct 1 1987 |

Event | 3rd Annual Symposium on Computational Geometry, SCG 1987 - Waterloo, Canada Duration: Jun 8 1987 → Jun 10 1987 |

### Other

Other | 3rd Annual Symposium on Computational Geometry, SCG 1987 |
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Country | Canada |

City | Waterloo |

Period | 6/8/87 → 6/10/87 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics

### Cite this

*Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987*(pp. 1-10). Association for Computing Machinery, Inc. https://doi.org/10.1145/41958.41959

**Computing the link center of a simple polygon.** / Lenhart, W.; Pollack, R.; Sack, J.; Seidel, R.; Shari, M.; Suri, S.; Toussaint, Godfried; Whitesides, S.; Yap, Chee.

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

*Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987.*Association for Computing Machinery, Inc, pp. 1-10, 3rd Annual Symposium on Computational Geometry, SCG 1987, Waterloo, Canada, 6/8/87. https://doi.org/10.1145/41958.41959

}

TY - GEN

T1 - Computing the link center of a simple polygon

AU - Lenhart, W.

AU - Pollack, R.

AU - Sack, J.

AU - Seidel, R.

AU - Shari, M.

AU - Suri, S.

AU - Toussaint, Godfried

AU - Whitesides, S.

AU - Yap, Chee

PY - 1987/10/1

Y1 - 1987/10/1

N2 - The link center of a simple polygon P is the set of points x inside P at which the maximal link-distancefrom x to any other point in P is minimized, where the link distance between two points x, y inside P isdefined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We proveseveral geometric properties of the link center and present an algorithm that calculates this set in time0(n2), where n is the number of sides of P. We also give an 0 (n log n) algorithm for finding apoint x in an approximate link center, namely the maximal link distance from x to any point in P is at most one more than the value attained from the link center.

AB - The link center of a simple polygon P is the set of points x inside P at which the maximal link-distancefrom x to any other point in P is minimized, where the link distance between two points x, y inside P isdefined as the smallest number of straight edges in a polygonal path inside P connecting x to y. We proveseveral geometric properties of the link center and present an algorithm that calculates this set in time0(n2), where n is the number of sides of P. We also give an 0 (n log n) algorithm for finding apoint x in an approximate link center, namely the maximal link distance from x to any point in P is at most one more than the value attained from the link center.

UR - http://www.scopus.com/inward/record.url?scp=85036466524&partnerID=8YFLogxK

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U2 - 10.1145/41958.41959

DO - 10.1145/41958.41959

M3 - Conference contribution

AN - SCOPUS:85036466524

SP - 1

EP - 10

BT - Proceedings of the 3rd Annual Symposium on Computational Geometry, SCG 1987

PB - Association for Computing Machinery, Inc

ER -