Minimum area polygons with two reflex angles enclosing k Points
We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are based on line sweep paradigm. The idea is to enumerate all the polygons in each kind and find the minimum one. We also analyse the complexiti...
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| Published in: | International journal of computer mathematics Vol. 77; no. 4; pp. 507 - 522 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Abingdon
Gordon and Breach Science Publishers
01.01.2001
Taylor and Francis |
| Subjects: | |
| ISSN: | 0020-7160, 1029-0265 |
| Online Access: | Get full text |
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| Abstract | We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are based on line sweep paradigm. The idea is to enumerate all the polygons in each kind and find the minimum one. We also analyse the complexities of each of the algorithms. We find that out of the four orthogonal polygons with two reflex angles, three are orthoconvex and the algorithms presented for these polygons work in
time, where n could be O(n-k)
3
in the worst case. The algorithm for the non-orthoconvex polygon has a complexity of
where n could be O((n-k)
3
n) in the worst case. |
|---|---|
| AbstractList | We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are based on line sweep paradigm. The idea is to enumerate all the polygons in each kind and find the minimum one. We also analyse the complexities of each of the algorithms. We find that out of the four orthogonal polygons with two reflex angles, three are orthoconvex and the algorithms presented for these polygons work in
time, where n could be O(n-k)
3
in the worst case. The algorithm for the non-orthoconvex polygon has a complexity of
where n could be O((n-k)
3
n) in the worst case. |
| Author | Krithivasan, Kamala Srilakshmi, Vanam |
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| Cites_doi | 10.1007/978-1-4612-1098-6 10.1515/9780773591134-006 10.1016/0196-6774(91)90022-Q |
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| Copyright | Copyright Taylor & Francis Group, LLC 2001 2002 INIST-CNRS |
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| Keywords | Computational geometry Isothetic polygon Minimum area polygon Computational complexity Optimization Orthoconvex polygon |
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| References | O'Rourke J. (CIT0008) 1987 Jeyalakshmi S. (CIT0005) 1998 CIT0001 Datta A. (CIT0002) 1993; 709 CIT0003 Preperata F.P. (CIT0009) 1985 CIT0004 CIT0007 CIT0006 |
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| Snippet | We present in this paper, algorithms for finding the minimum area isothetic polygons having two reflex angles containing k points; (k<n) Our algorithms are... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Computer science; control theory; systems Convex and discrete geometry Exact sciences and technology F.2.2[Analysis of Algorithms and Problem Complexity] Geometry I.3.5[Computational Geometry and Object Modeling] Isothetic polygon with reflex angles Line sweep paradigm Mathematics Methods of scientific computing (including symbolic computation, algebraic computation) Minimum area polygon Numerical analysis Numerical analysis. Scientific computation Numerical methods in probability and statistics Optimization problem Orthoconvex polygon Polygon enclosing points Sciences and techniques of general use Theoretical computing |
| Title | Minimum area polygons with two reflex angles enclosing k Points |
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