### Abstract

Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n^{2}). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.

Original language | English (US) |
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Title of host publication | Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985 |

Publisher | Association for Computing Machinery, Inc |

Pages | 1-7 |

Number of pages | 7 |

ISBN (Electronic) | 0897911636, 9780897911634 |

DOIs | |

State | Published - Jun 1 1985 |

Event | 1st Annual Symposium on Computational Geometry, SCG 1985 - Baltimore, United States Duration: Jun 5 1985 → Jun 7 1985 |

### Other

Other | 1st Annual Symposium on Computational Geometry, SCG 1985 |
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Country | United States |

City | Baltimore |

Period | 6/5/85 → 6/7/85 |

### Fingerprint

### ASJC Scopus subject areas

- Computational Mathematics
- Geometry and Topology

### Cite this

*Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985*(pp. 1-7). Association for Computing Machinery, Inc. https://doi.org/10.1145/323233.323234

**Computing the width of a set.** / Houle, Michael B.; Toussaint, Godfried.

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

*Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985.*Association for Computing Machinery, Inc, pp. 1-7, 1st Annual Symposium on Computational Geometry, SCG 1985, Baltimore, United States, 6/5/85. https://doi.org/10.1145/323233.323234

}

TY - GEN

T1 - Computing the width of a set

AU - Houle, Michael B.

AU - Toussaint, Godfried

PY - 1985/6/1

Y1 - 1985/6/1

N2 - Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n2). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.

AB - Given a set of points P - {p1,p2....Pn} ,n three dimensions, the width of P, W(P)% is defined as the minimum distance between parallel planes of support of P. It is shown that W(P) can be computed in O(n logn time and O(n) space, where / is the number of antipodal pairs? of edges of the convex hull of P, and in the worst case O(n2). [f P is a set of points in the plane, this complexity can be reduced to O(n logn). Finally, for simple polygons linear time suffices.

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U2 - 10.1145/323233.323234

DO - 10.1145/323233.323234

M3 - Conference contribution

SP - 1

EP - 7

BT - Proceedings of the 1st Annual Symposium on Computational Geometry, SCG 1985

PB - Association for Computing Machinery, Inc

ER -