### Abstract

The paper presents an extension of the work of Bern on tetrahedralization, which is the triangulation of three dimensional polyhedra or the region between them. Attention is given on Steiner points which are additional vertices for nonconvex polyhedra to be tetrahedralized. A linear algorithm was given for the triangulation in the region between two polyhedra, and the region between a convex polyhedron and a disjoint polyhedral terrain. It was proven that any polyhedron of genus g must have at least g-1 reflex dihedral angles.

Original language | English (US) |
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Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Publisher | Publ by ACM |

Pages | 231-239 |

Number of pages | 9 |

ISBN (Print) | 0897916484, 9780897916486 |

DOIs | |

State | Published - Jan 1 1994 |

Event | Proceedings of the 10th Annual Symposium on Computational Geometry - Stony Brook, NY, USA Duration: Jun 6 1994 → Jun 8 1994 |

### Publication series

Name | Proceedings of the Annual Symposium on Computational Geometry |
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### Other

Other | Proceedings of the 10th Annual Symposium on Computational Geometry |
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City | Stony Brook, NY, USA |

Period | 6/6/94 → 6/8/94 |

### All Science Journal Classification (ASJC) codes

- Software
- Geometry and Topology
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

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## Cite this

Chazelle, B., & Shouraboura, N. (1994). Bounds on the size of tetrahedralizations. In

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 231-239). (Proceedings of the Annual Symposium on Computational Geometry). Publ by ACM. https://doi.org/10.1145/177424.177975