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A space–time trade-off for computing the visibility polygon in the multi-pass model

  • Mohammad Asgaripour
  • Ali MohadesEmail author
Foundations
  • 4 Downloads

Abstract

We study the problem of computing the visibility polygon of a simple polygon \({\mathcal {P}}\) from a viewpoint inside it, when \({\mathcal {P}}\) resides in a read-only memory without random accessibility. This model of stored data is called the multi-pass model in the literature. We present an algorithm to compute the visibility polygon in this model in \(O(nr/t + nt)\) time, where n is the size of input data, r is the number of reflex vertices of input data, and t is the number of additional variables which we use to compute the visibility polygon where \(2<t<r\).

Keywords

Visibility polygon Limited memory Multi-pass model 

Notes

Compliance with ethical standards

Conflict of interest

M. Asgaripour declares that he has no conflict of interest. A. Mohades declares that he has no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animal performed by any of authors.

References

  1. Bahoo Y, Banyassady B, Bose P, Durocher S, Mulzer W (2016) Time–space trade-off for finding the \(k\)-visibility region of a point in a polygon. CoRR arXiv:1603.02853
  2. Barba L, Korman M, Langerman S, Silveira RI (2011) Computing the visibility polygon using few variables. Springer, Berlin, pp 70–79zbMATHGoogle Scholar
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  4. Zarrabi-Zadeh H, Chan TM (2006) A simple streaming algorithm for minimum enclosing balls. In: Proceedings of the 18th Canadian conference on computational geometry, pp 139–142Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Algorithms and Computational GeometryAmirkabir University of TechnologyTehranIran

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