Location of a Point in a Planar Subdivision and Its Application.
Abstract
Given a subdivision of the plane induced by a planar graph with n vertices, in this paper we consider the problem of identifying which region of the subdivision contains a given test point. We present a search algorithm, called point-location algorithm, which operates on a suitably preprocessed data structure. The search runs in time at most 0(log4sub 25n) sq.), while the preprocessing task runs in time at most 0(n4log sub25n) and requires 0(n) storage. The methods are quite general, since an arbitrary subdivision can be transformed in time at most 0(n log n) into one to which the preprocessing procedure is applicable. This solution of the point location problem yields interesting and efficient solutions of other geometric problems, such as spatial convex inclusion and inclusion in an arbitrary polygon. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1975
- Accession Number
- ADA019448
Entities
People
- D. T. Lee
- Franco P. Preparata
Organizations
- University of Illinois Urbana–Champaign