### Abstract

Let S be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in S where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time O(1 + min(log 1/Δ_{p}, log n)), where Δ_{p} is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area Ω(δ _{p}
^{2}).

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings |

Pages | 49-60 |

Number of pages | 12 |

Volume | 8037 LNCS |

DOIs | |

State | Published - 2013 |

Event | 13th International Symposium on Algorithms and Data Structures, WADS 2013 - London, ON, Canada Duration: Aug 12 2013 → Aug 14 2013 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 8037 LNCS |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 13th International Symposium on Algorithms and Data Structures, WADS 2013 |
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Country | Canada |

City | London, ON |

Period | 8/12/13 → 8/14/13 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings*(Vol. 8037 LNCS, pp. 49-60). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8037 LNCS). https://doi.org/10.1007/978-3-642-40104-6_5

**Distance-sensitive planar point location.** / Aronov, Boris; De Berg, Mark; Roeloffzen, Marcel; Speckmann, Bettina.

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

*Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings.*vol. 8037 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8037 LNCS, pp. 49-60, 13th International Symposium on Algorithms and Data Structures, WADS 2013, London, ON, Canada, 8/12/13. https://doi.org/10.1007/978-3-642-40104-6_5

}

TY - GEN

T1 - Distance-sensitive planar point location

AU - Aronov, Boris

AU - De Berg, Mark

AU - Roeloffzen, Marcel

AU - Speckmann, Bettina

PY - 2013

Y1 - 2013

N2 - Let S be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in S where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time O(1 + min(log 1/Δp, log n)), where Δp is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area Ω(δ p 2).

AB - Let S be a connected planar polygonal subdivision with n edges and of total area 1. We present a data structure for point location in S where queries with points far away from any region boundary are answered faster. More precisely, we show that point location queries can be answered in time O(1 + min(log 1/Δp, log n)), where Δp is the distance of the query point p to the boundary of the region containing p. Our structure is based on the following result: any simple polygon P can be decomposed into a linear number of convex quadrilaterals with the following property: for any point p ∈ P, the quadrilateral containing p has area Ω(δ p 2).

UR - http://www.scopus.com/inward/record.url?scp=84881161555&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881161555&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-40104-6_5

DO - 10.1007/978-3-642-40104-6_5

M3 - Conference contribution

SN - 9783642401039

VL - 8037 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 49

EP - 60

BT - Algorithms and Data Structures - 13th International Symposium, WADS 2013, Proceedings

ER -