Capturing Points with a Rotating Polygon (and a 3D Extension)

We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a segment or a line. We also solve an extension to 3D where we rotate a polyhe...

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Vydané v:Theory of computing systems Ročník 63; číslo 3; s. 543 - 566
Hlavní autori: Alegría-Galicia, Carlos, Orden, David, Palios, Leonidas, Seara, Carlos, Urrutia, Jorge
Médium: Journal Article Publikácia
Jazyk:English
Vydavateľské údaje: New York Springer US 01.04.2019
Springer Nature B.V
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ISSN:1432-4350, 1433-0490, 1433-0490
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Abstract We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a segment or a line. We also solve an extension to 3D where we rotate a polyhedron around a given point to contain the maximum number of elements from a set of points in the space.
AbstractList This is a post-peer-review, pre-copyedit version of an article published in Theory of computing systems: an international journal. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00224-018-9885-y We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a segment or a line. We also solve an extension to 3D where we rotate a polyhedron around a given point to contain the maximum number of elements from a set of points in the space. Peer Reviewed
We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a segment or a line. We also solve an extension to 3D where we rotate a polyhedron around a given point to contain the maximum number of elements from a set of points in the space.
Author Alegría-Galicia, Carlos
Seara, Carlos
Orden, David
Palios, Leonidas
Urrutia, Jorge
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  givenname: Leonidas
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  fullname: Palios, Leonidas
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  givenname: Carlos
  surname: Seara
  fullname: Seara, Carlos
  organization: Departament de Matemàtiques, Universitat Politècnica de Catalunya
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Cites_doi 10.1145/3185378
10.1007/s00453-007-9036-3
10.1016/S0925-7721(98)00015-7
10.1109/34.121792
10.1016/S0925-7721(96)00011-9
10.1016/0925-7721(95)00022-2
10.1016/j.comgeo.2013.10.003
10.1142/S0218195901000596
10.1016/S0925-7721(01)00041-4
10.1137/1.9781611974331.ch89
10.1145/1806689.1806772
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Contributor Universitat Politècnica de Catalunya. CGA -Computational Geometry and Applications
Universitat Politècnica de Catalunya. Departament de Matemàtiques
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Theory of Computing Systems is a copyright of Springer, (2018). All Rights Reserved.
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Issue 3
Keywords Polyhedron
Geometric optimization
Points covering
Polygon
Rotation
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– ident: 9885_CR14
  doi: 10.1145/1806689.1806772
– volume: 50
  start-page: 584
  issue: 4
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  publication-title: Algorithmica
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– ident: 9885_CR7
– volume: 14
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  issue: 2
  year: 1992
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  publication-title: IEEE Trans. Pattern Anal. Mach. Intell.
  doi: 10.1109/34.121792
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  issue: 3
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  ident: 9885_CR9
  publication-title: Comput. Geom. Theory nd Appl.
  doi: 10.1016/0925-7721(95)00022-2
– volume: 47
  start-page: 407
  issue: 3, Part A
  year: 2014
  ident: 9885_CR5
  publication-title: Comput. Geom. Theory Appl.
  doi: 10.1016/j.comgeo.2013.10.003
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Snippet We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this...
This is a post-peer-review, pre-copyedit version of an article published in Theory of computing systems: an international journal. The final authenticated...
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StartPage 543
SubjectTerms 11 Number theory
11C Polynomials and matrices
26 Real functions
26C Polynomials, rational functions
Anàlisi matemàtica
Classificació AMS
Computer Science
Geometric optimization
Matemàtiques i estadística
Points covering
Polinomis
Polygon
Polyhedron
Polynomials
Rotation
Teoria de nombres
Theory of Computation
Àlgebra
Àrees temàtiques de la UPC
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Title Capturing Points with a Rotating Polygon (and a 3D Extension)
URI https://link.springer.com/article/10.1007/s00224-018-9885-y
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https://recercat.cat/handle/2072/364102
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