### Abstract

In this paper, we give an algorithm for output-sensitn construction of an f-face polytope that is defined by halfspaces in E^{4}. Our algorithm runs in O((n + /)log^{2} ) time and uses 0(n + f) space. This is the first algorithi within a polylogarithmic factor of optimal 0(n logf/ + f) time over the whole range of f. By a standard liftir map, we obtain output-sensitive algorithms for the Voroni diagram or Delaunay triangulation in E^{3} and for the portic of a Voronoi diagram that is clipped to a convex polytop Our approach also simplifies the "ultimate convex hn algorithm" of Kirkpatrick and Seidel in E^{2}.

Original language | English (US) |
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Title of host publication | Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |

Publisher | Association for Computing Machinery |

Pages | 282-291 |

Number of pages | 10 |

Volume | Part F129524 |

ISBN (Electronic) | 0898713498 |

State | Published - Jan 22 1995 |

Event | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 - San Francisco, United States Duration: Jan 22 1995 → Jan 24 1995 |

### Other

Other | 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995 |
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Country | United States |

City | San Francisco |

Period | 1/22/95 → 1/24/95 |

### Fingerprint

### ASJC Scopus subject areas

- Software
- Mathematics(all)

### Cite this

*Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995*(Vol. Part F129524, pp. 282-291). Association for Computing Machinery.

**Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three.** / Chan, Timothy M.Y.; Snoeyink, Jack; Yap, Chee.

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

*Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995.*vol. Part F129524, Association for Computing Machinery, pp. 282-291, 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995, San Francisco, United States, 1/22/95.

}

TY - GEN

T1 - Output-sensitive construction of polytopes in four dimensions and clipped Voronoi diagrams in three

AU - Chan, Timothy M.Y.

AU - Snoeyink, Jack

AU - Yap, Chee

PY - 1995/1/22

Y1 - 1995/1/22

N2 - In this paper, we give an algorithm for output-sensitn construction of an f-face polytope that is defined by halfspaces in E4. Our algorithm runs in O((n + /)log2 ) time and uses 0(n + f) space. This is the first algorithi within a polylogarithmic factor of optimal 0(n logf/ + f) time over the whole range of f. By a standard liftir map, we obtain output-sensitive algorithms for the Voroni diagram or Delaunay triangulation in E3 and for the portic of a Voronoi diagram that is clipped to a convex polytop Our approach also simplifies the "ultimate convex hn algorithm" of Kirkpatrick and Seidel in E2.

AB - In this paper, we give an algorithm for output-sensitn construction of an f-face polytope that is defined by halfspaces in E4. Our algorithm runs in O((n + /)log2 ) time and uses 0(n + f) space. This is the first algorithi within a polylogarithmic factor of optimal 0(n logf/ + f) time over the whole range of f. By a standard liftir map, we obtain output-sensitive algorithms for the Voroni diagram or Delaunay triangulation in E3 and for the portic of a Voronoi diagram that is clipped to a convex polytop Our approach also simplifies the "ultimate convex hn algorithm" of Kirkpatrick and Seidel in E2.

UR - http://www.scopus.com/inward/record.url?scp=0039173487&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039173487&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0039173487

VL - Part F129524

SP - 282

EP - 291

BT - Proceedings of the 6th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 1995

PB - Association for Computing Machinery

ER -