About the Book

The Stony Brook Algorithm Repository

Steven Skiena
Stony Brook University
Dept. of Computer Science

1.6.7 Point Location

INPUT                    OUTPUT

Input Description: A decomposition of the plane into polygonal regions, and a query point q.

Problem: Which region contains the query point q?

Excerpt from The Algorithm Design Manual: Point location is a fundamental subproblem in computational geometry, usually needed as an ingredient to solve larger geometric problems. In a dispatch system to assign policemen to the scene of a crime, the city will be partitioned into different precincts or districts. Given a map of regions and a query point (the crime scene), the system must identify which region contains the point. This is exactly the problem of planar point location.

Implementations

CGAL: The Computational Geometry Algorithms Library (C++) (rating 8)

LEDA - A Library of Efficient Data Types and Algorithms (C++) (rating 8)

ANN - Approximate Nearest Neighbors (C++) (rating 7)

Arrange - maintainance of arrangements with point location (C) (rating 5)

3D Convex Hull algorithm in Java (C) (rating 3)

Moret and Shapiro's Algorithms P to NP (Pascal) (rating 2)

Recommended Books

Computational Geometry : Algorithms and Applications by Mark De Berg, Marc Van Kreveld, Mark Overmars, and O. Schwartskopf	Computational Geometry in C by Joseph O'Rourke	Algorithms from P to NP, Vol. I: Design and Efficiency by B. Moret and H. Shapiro
Introduction to Algorithms by U. Manber	Computational Geometry by F. Preparata and M. Shamos

Kd-Trees	Maintaining Line Arrangements	Nearest Neighbor Search
Range Search	Voronoi Diagrams

The Stony Brook Algorithm Repository

1.6.7 Point Location

INPUT OUTPUT

Implementations

Recommended Books

Related Problems