### Abstract

We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k^{3}+kn log^{2} k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k^{3}+kn log^{3} k) expected time.

Original language | English (US) |
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Title of host publication | Annual Symposium on Foundatons of Computer Science (Proceedings) |

Editors | Anon |

Publisher | Publ by IEEE |

Pages | 518-527 |

Number of pages | 10 |

ISBN (Print) | 0818643706 |

State | Published - 1993 |

Event | Proceedings of the 34th Annual Symposium on Foundations of Computer Science - Palo Alto, CA, USA Duration: Nov 3 1993 → Nov 5 1993 |

### Other

Other | Proceedings of the 34th Annual Symposium on Foundations of Computer Science |
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City | Palo Alto, CA, USA |

Period | 11/3/93 → 11/5/93 |

### ASJC Scopus subject areas

- Hardware and Architecture

### Cite this

*Annual Symposium on Foundatons of Computer Science (Proceedings)*(pp. 518-527). Publ by IEEE.

**Union of convex polyhedra in three dimensions.** / Aronov, Boris; Sharir, Micha.

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

*Annual Symposium on Foundatons of Computer Science (Proceedings).*Publ by IEEE, pp. 518-527, Proceedings of the 34th Annual Symposium on Foundations of Computer Science, Palo Alto, CA, USA, 11/3/93.

}

TY - GEN

T1 - Union of convex polyhedra in three dimensions

AU - Aronov, Boris

AU - Sharir, Micha

PY - 1993

Y1 - 1993

N2 - We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3+kn log2 k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k3+kn log3 k) expected time.

AB - We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3+kn log2 k). This bound is almost tight in the worst case. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k3+kn log3 k) expected time.

UR - http://www.scopus.com/inward/record.url?scp=0027842565&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027842565&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0027842565

SN - 0818643706

SP - 518

EP - 527

BT - Annual Symposium on Foundatons of Computer Science (Proceedings)

A2 - Anon, null

PB - Publ by IEEE

ER -