A Dynamic Data Structure to Efficiently Find the Points below a Line and Estimate Their Number
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 )...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2017-03-01
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| Series: | ISPRS International Journal of Geo-Information |
| Subjects: | |
| Online Access: | http://www.mdpi.com/2220-9964/6/3/82 |
| Summary: | 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. |
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| ISSN: | 2220-9964 |