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Theory of Computing Systems

, Volume 63, Issue 3, pp 543–566 | Cite as

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

  • Carlos Alegría-Galicia
  • David OrdenEmail author
  • Leonidas Palios
  • Carlos Seara
  • Jorge Urrutia
Article

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.

Keywords

Points covering Rotation Geometric optimization Polygon Polyhedron 

Notes

Acknowledgements

David Orden is supported by MINECO Projects with references MTM2014-54207 and MTM2017-83750-P, as well as by H2020-MSCA-RISE project 734922 - CONNECT. Carlos Seara is supported by projects Gen. Cat. DGR 2017SGR1640, MINECO/FEDER MTM2015-63791-R, and by H2020-MSCA-RISE project 734922 - CONNECT. Jorge Urrutia is supported in part by SEP-CONACYT of México, Proyecto 80268, and by PAPPIIT IN102117 Programa de Apoyo a la Investigación e Innovación Tecnológica, Universidad Nacional Autónoma de México.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Posgrado en Ciencia e Ingeniería de la ComputaciónUniversidad Nacional Autónoma de MéxicoMexico CityMéxico
  2. 2.Departamento de Física y MatemáticasUniversidad de AlcaláMadridSpain
  3. 3.Department of Computer Science and EngineeringUniversity of IoanninaIoanninaGreece
  4. 4.Departament de MatemàtiquesUniversitat Politècnica de CatalunyaBarcelonaSpain
  5. 5.Instituto de MatemáticasUniversidad Nacional Autónoma de MéxicoMexico CityMéxico

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