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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Bibliographic Details
Published in:Theory of computing systems Vol. 63; no. 3; pp. 543 - 566
Main Authors: Alegría-Galicia, Carlos, Orden, David, Palios, Leonidas, Seara, Carlos, Urrutia, Jorge
Format: Journal Article Publication
Language:English
Published: New York Springer US 01.04.2019
Springer Nature B.V
Subjects:
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
Polyhedron
Geometric optimization
Points covering
Polygon
Rotation
ISSN:1432-4350, 1433-0490, 1433-0490
Online Access:Get full text
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Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1432-4350
1433-0490
1433-0490
DOI:10.1007/s00224-018-9885-y