### Abstract

Given a set P of n points in the plane in general position, and a set of non-crossing segments with endpoints in P, we seek to place a new point q such that the constrained Delaunay triangulation of P ∪ {q} has the largest possible minimum angle. The expected running time of our (randomized) algorithm is O(n^{2} log n) on any input, improving the near-cubic time of the best previously known algorithm. Our algorithm is somewhat complex, and along the way we develop a simpler cubic-time algorithm quite different from the ones already known.

Original language | English (US) |
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Pages | 395-400 |

Number of pages | 6 |

State | Published - 2014 |

Event | 26th Canadian Conference on Computational Geometry, CCCG 2014 - Halifax, Canada Duration: Aug 11 2014 → Aug 13 2014 |

### Other

Other | 26th Canadian Conference on Computational Geometry, CCCG 2014 |
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Country | Canada |

City | Halifax |

Period | 8/11/14 → 8/13/14 |

### ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics

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## Cite this

Aronov, B., & Yagnatinsky, M. (2014).

*Quickly placing a point to maximize angles*. 395-400. Paper presented at 26th Canadian Conference on Computational Geometry, CCCG 2014, Halifax, Canada.