### 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 in r, 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 log r) time.

Original language | English (US) |
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Pages (from-to) | 245-265 |

Number of pages | 21 |

Journal | Algorithmica (New York) |

Volume | 17 |

Issue number | 3 |

DOIs | |

State | Published - Mar 1997 |

### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Computer Science Applications
- Applied Mathematics

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## Cite this

Chazelle, B., & Palios, L. (1997). Decomposing the Boundary of a Nonconvex Polyhedron.

*Algorithmica (New York)*,*17*(3), 245-265. https://doi.org/10.1007/BF02523191