Determining sector visibility of a polygon

B. Bhattacharya, D. G. Kirkpatrick, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a generalization of notions of external visibility of simple polygons, namely weak external visibility, weak external visibility from a line and monotonicity, that we call sector visibility. Informally, sector visibility addresses the question of external visibility along rays (or sight lines) whose angles are restricted to a sector (wedge) of specified width u. This provides an interesting measure of the degree of external visibility of a polygon. Our framework also permits a unification and extension of a number of previously unrelated results. Finally, our results uncover a curious complexity discontinuity in this family of problems; algorithms are θ(n) when γ < φ or γ = 2φr, but require ω(n log n) time (at least), when φ < u < 2φ.

Original languageEnglish (US)
Title of host publicationProceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989
PublisherAssociation for Computing Machinery
Pages247-254
Number of pages8
VolumePart F130124
ISBN (Electronic)0897913183
DOIs
StatePublished - Jun 5 1989
Event5th Annual Symposium on Computational Geometry, SCG 1989 - Saarbruchen, Germany
Duration: Jun 5 1989Jun 7 1989

Other

Other5th Annual Symposium on Computational Geometry, SCG 1989
CountryGermany
CitySaarbruchen
Period6/5/896/7/89

Fingerprint

Visibility
Polygon
Sector
Simple Polygon
Line
Wedge
Unification
Monotonicity
Half line
Discontinuity
Angle

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Bhattacharya, B., Kirkpatrick, D. G., & Toussaint, G. (1989). Determining sector visibility of a polygon. In Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989 (Vol. Part F130124, pp. 247-254). Association for Computing Machinery. https://doi.org/10.1145/73833.73860

Determining sector visibility of a polygon. / Bhattacharya, B.; Kirkpatrick, D. G.; Toussaint, Godfried.

Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124 Association for Computing Machinery, 1989. p. 247-254.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bhattacharya, B, Kirkpatrick, DG & Toussaint, G 1989, Determining sector visibility of a polygon. in Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. vol. Part F130124, Association for Computing Machinery, pp. 247-254, 5th Annual Symposium on Computational Geometry, SCG 1989, Saarbruchen, Germany, 6/5/89. https://doi.org/10.1145/73833.73860
Bhattacharya B, Kirkpatrick DG, Toussaint G. Determining sector visibility of a polygon. In Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124. Association for Computing Machinery. 1989. p. 247-254 https://doi.org/10.1145/73833.73860
Bhattacharya, B. ; Kirkpatrick, D. G. ; Toussaint, Godfried. / Determining sector visibility of a polygon. Proceedings of the 5th Annual Symposium on Computational Geometry, SCG 1989. Vol. Part F130124 Association for Computing Machinery, 1989. pp. 247-254
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