### Abstract

We show how to triangulate an n-vertex polygonal region - adding extra vertices as necessary - with triangles of guaranteed quality. Using only O(n) triangles, we can guarantee that the smallest height (shortest dimension) of a triangle is approximately as large as possible. Using O(n log n) triangles, we can also guarantee that the largest angle is no greater than 150°. Finally we give a nonobtuse triangulation algorithm for convex polygons that uses O(n^{1.85}) triangles.

Original language | English (US) |
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Title of host publication | Eighth Annual Symposium On Computational Geometry |

Publisher | Publ by ACM |

Pages | 222-231 |

Number of pages | 10 |

ISBN (Print) | 0897915178, 9780897915175 |

DOIs | |

State | Published - Jan 1 1992 |

Externally published | Yes |

Event | Eighth Annual Symposium On Computational Geometry - Berlin, Ger Duration: Jun 10 1992 → Jun 12 1992 |

### Publication series

Name | Eighth Annual Symposium On Computational Geometry |
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### Other

Other | Eighth Annual Symposium On Computational Geometry |
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City | Berlin, Ger |

Period | 6/10/92 → 6/12/92 |

### All Science Journal Classification (ASJC) codes

- Engineering(all)

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## Cite this

Bern, M., Dobkin, D., & Eppstein, D. (1992). Triangulating polygons without large angles. In

*Eighth Annual Symposium On Computational Geometry*(pp. 222-231). (Eighth Annual Symposium On Computational Geometry). Publ by ACM. https://doi.org/10.1145/142675.142722