### 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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Title of host publication | 26th Canadian Conference on Computational Geometry, CCCG 2014 |

Publisher | Canadian Conference on Computational Geometry |

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 |
---|---|

Country | Canada |

City | Halifax |

Period | 8/11/14 → 8/13/14 |

### Fingerprint

### ASJC Scopus subject areas

- Geometry and Topology
- Computational Mathematics

### Cite this

*26th Canadian Conference on Computational Geometry, CCCG 2014*(pp. 395-400). Canadian Conference on Computational Geometry.

**Quickly placing a point to maximize angles.** / Aronov, Boris; Yagnatinsky, Mark.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*26th Canadian Conference on Computational Geometry, CCCG 2014.*Canadian Conference on Computational Geometry, pp. 395-400, 26th Canadian Conference on Computational Geometry, CCCG 2014, Halifax, Canada, 8/11/14.

}

TY - GEN

T1 - Quickly placing a point to maximize angles

AU - Aronov, Boris

AU - Yagnatinsky, Mark

PY - 2014

Y1 - 2014

N2 - 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(n2 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.

AB - 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(n2 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.

UR - http://www.scopus.com/inward/record.url?scp=84961331163&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961331163&partnerID=8YFLogxK

M3 - Conference contribution

SP - 395

EP - 400

BT - 26th Canadian Conference on Computational Geometry, CCCG 2014

PB - Canadian Conference on Computational Geometry

ER -