Computer Science and Engineering, Department of


Date of this Version



ISPRS Int. J. Geo-Inf. 2017, 6, 82; doi:10.3390/ijgi6030082.


Copyright © 2017, the authors. Licensee MDPI, Basel, Switzerland. Open access, Creative Commons Attribution license 4.0.


A basic question in computational geometry is how to find the relationship between a set of points and a line in a real plane. In this paper, we present multidimensional data structures for N points that allow answering the following queries for any given input line: (1) estimate in O(log N) time the number of points below the line; (2) return in O(log N + k) time the k ≤ N points that are below the line; and (3) return in O(log N) time the point that is closest to the line. We illustrate the utility of this computational question with GIS applications in air defense and traffic control.