A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
UHasselt–Hasselt University and transnational University Limburg, Databases and Theoretical Computer Science Research Group, Agoralaan, Gebouw D, Diepenbeek 3590, Belgium
Department of Computer Science & Engineering, University of Nebraska-Lincoln, 256 Avery Hall, 1144 T Street, Lincoln, NE 68588-0115, USA
Author to whom correspondence should be addressed.
Academic Editor: Wolfgang Kainz
Received: 1 February 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 15 March 2017
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
time the number of points below the line; (2) return in
points that are below the line; and (3) return in
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.
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MDPI and ACS Style
Kuijpers, B.; Revesz, P.Z. A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number. ISPRS Int. J. Geo-Inf. 2017, 6, 82.
Kuijpers B, Revesz PZ. A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number. ISPRS International Journal of Geo-Information. 2017; 6(3):82.
Kuijpers, Bart; Revesz, Peter Z. 2017. "A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number." ISPRS Int. J. Geo-Inf. 6, no. 3: 82.
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