### 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) |
---|---|

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 - Dec 1 1993 |

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

### Publication series

Name | Annual Symposium on Foundatons of Computer Science (Proceedings) |
---|---|

ISSN (Print) | 0272-5428 |

### Other

Other | Proceedings of the 34th Annual Symposium on Foundations of Computer Science |
---|---|

City | Palo Alto, CA, USA |

Period | 11/3/93 → 11/5/93 |

### ASJC Scopus subject areas

- Hardware and Architecture

## Cite this

Aronov, B., & Sharir, M. (1993). Union of convex polyhedra in three dimensions. In Anon (Ed.),

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