### Abstract

A new data structure is presented for planar point location that executes a point location query quickly if it is spatially near the previous query. Given a triangulation T of size n and a sequence of point location queries A = q_{1}, . . . q_{m}, the structure presented executes q_{i} in time O(log d(q_{i-1}, q_{i})). The distance function, d, that is used is a two dimensional generalization of rank distance that counts the number of triangles in a region from q_{i-1} to q_{i}. The data structure uses O(n log log n) space.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the Annual Symposium on Computational Geometry |

Pages | 220-226 |

Number of pages | 7 |

State | Published - 2003 |

Event | Nineteenth Annual Symposium on Computational Geometry - san Diego, CA, United States Duration: Jun 8 2003 → Jun 10 2003 |

### Other

Other | Nineteenth Annual Symposium on Computational Geometry |
---|---|

Country | United States |

City | san Diego, CA |

Period | 6/8/03 → 6/10/03 |

### Fingerprint

### Keywords

- Planar point location

### ASJC Scopus subject areas

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

### Cite this

*Proceedings of the Annual Symposium on Computational Geometry*(pp. 220-226)

**Proximate planar point location.** / Iacono, John; Langerman, Stefan.

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

*Proceedings of the Annual Symposium on Computational Geometry.*pp. 220-226, Nineteenth Annual Symposium on Computational Geometry, san Diego, CA, United States, 6/8/03.

}

TY - GEN

T1 - Proximate planar point location

AU - Iacono, John

AU - Langerman, Stefan

PY - 2003

Y1 - 2003

N2 - A new data structure is presented for planar point location that executes a point location query quickly if it is spatially near the previous query. Given a triangulation T of size n and a sequence of point location queries A = q1, . . . qm, the structure presented executes qi in time O(log d(qi-1, qi)). The distance function, d, that is used is a two dimensional generalization of rank distance that counts the number of triangles in a region from qi-1 to qi. The data structure uses O(n log log n) space.

AB - A new data structure is presented for planar point location that executes a point location query quickly if it is spatially near the previous query. Given a triangulation T of size n and a sequence of point location queries A = q1, . . . qm, the structure presented executes qi in time O(log d(qi-1, qi)). The distance function, d, that is used is a two dimensional generalization of rank distance that counts the number of triangles in a region from qi-1 to qi. The data structure uses O(n log log n) space.

KW - Planar point location

UR - http://www.scopus.com/inward/record.url?scp=0038038272&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0038038272&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0038038272

SP - 220

EP - 226

BT - Proceedings of the Annual Symposium on Computational Geometry

ER -