### Abstract

We show that the boundary of a three-dimensional polyhedron with r reflex angles and arbitrary genus can be subdivided into O(r) connected pieces, each of which lies on the boundary of its convex hull. A remarkable feature of this result is that the number of these convex-like pieces is independent of the number of vertices. Furthermore, it is linear inr, which contrasts with a quadratic worst-case lower bound in the number of convex pieces needed to decompose the polyhedron itself. The number of new vertices introduced in the process is O(n). The decomposition can be computed in O(n + r logr) time.

Original language | English (US) |
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Title of host publication | Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings |

Editors | Otto Nurmi, Esko Ukkonen |

Publisher | Springer Verlag |

Pages | 364-375 |

Number of pages | 12 |

ISBN (Print) | 9783540557067 |

DOIs | |

State | Published - Jan 1 1992 |

Event | 3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992 - Helsinki, Finland Duration: Jul 8 1992 → Jul 10 1992 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 621 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 3rd Scandinavian Workshop on Algorithm Theory, SWAT 1992 |
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Country | Finland |

City | Helsinki |

Period | 7/8/92 → 7/10/92 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

Chazelle, B., & Palios, L. (1992). Decomposing the boundary of a nonconvex polyhedron. In O. Nurmi, & E. Ukkonen (Eds.),

*Algorithm Theory – SWAT 1992 - 3rd Scandinavian Workshop on Algorithm Theory, Proceedings*(pp. 364-375). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 621 LNCS). Springer Verlag. https://doi.org/10.1007/3-540-55706-7_33