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Determining sector visibility of a polygon

Authors:

B. Bhattacharya,

D. Kirkpatrick,

G. ToussaintAuthors Info & Claims

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

Pages 247 - 253

https://doi.org/10.1145/73833.73861

Published: 05 June 1989 Publication History

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 σ. 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 σ ≤ π or σ = 2π, but require Ω(n log n) time (at least), when π < σ < 2π.

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Cited By

BHATTACHARYA BMUKHOPADHYAY ATOUSSAINT G(2011)COMPUTING A SHORTEST WEAKLY EXTERNALLY VISIBLE LINE SEGMENT FOR A SIMPLE POLYGONInternational Journal of Computational Geometry & Applications10.1142/S021819599900007809:01(81-96)Online publication date: 20-Nov-2011
https://doi.org/10.1142/S0218195999000078
Chen D(2005)Optimally computing the shortest weakly visible subedge of a simple polygon preliminary versionAlgorithms and Computation10.1007/3-540-57568-5_263(323-332)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-57568-5_263
Berg MGuibas LHalperin DOvermars MSchwarzkopf OSharir MTeillaud M(2005)Reaching a goal with directional uncertaintyAlgorithms and Computation10.1007/3-540-57568-5_229(1-10)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-57568-5_229
Show More Cited By

Index Terms

Determining sector visibility of a polygon
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
      1. Computer vision representations
2. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory

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Published In

cover image ACM Conferences

SCG '89: Proceedings of the fifth annual symposium on Computational geometry

June 1989

401 pages

ISBN:0897913183

DOI:10.1145/73833

Chairman:
Kurt Mehlhorn

Copyright © 1989 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 05 June 1989

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

BHATTACHARYA BMUKHOPADHYAY ATOUSSAINT G(2011)COMPUTING A SHORTEST WEAKLY EXTERNALLY VISIBLE LINE SEGMENT FOR A SIMPLE POLYGONInternational Journal of Computational Geometry & Applications10.1142/S021819599900007809:01(81-96)Online publication date: 20-Nov-2011
https://doi.org/10.1142/S0218195999000078
Chen D(2005)Optimally computing the shortest weakly visible subedge of a simple polygon preliminary versionAlgorithms and Computation10.1007/3-540-57568-5_263(323-332)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-57568-5_263
Berg MGuibas LHalperin DOvermars MSchwarzkopf OSharir MTeillaud M(2005)Reaching a goal with directional uncertaintyAlgorithms and Computation10.1007/3-540-57568-5_229(1-10)Online publication date: 1-Jun-2005
https://doi.org/10.1007/3-540-57568-5_229
Bhattacharya BToussaint G(2005)Computing shortest transversalsAutomata, Languages and Programming10.1007/3-540-54233-7_171(649-660)Online publication date: 8-Jun-2005
https://doi.org/10.1007/3-540-54233-7_171
Briggs ADonald B(1994)Automatic sensor configuration for task-directed planningProceedings of the 1994 IEEE International Conference on Robotics and Automation10.1109/ROBOT.1994.351301(1345-1350)Online publication date: 1994
https://doi.org/10.1109/ROBOT.1994.351301
Bhattacharya BMukhopadhyay AToussaint G(1991)A linear time algorithm for computing the shortest line segment from which a polygon is weakly externally visibleAlgorithms and Data Structures10.1007/BFb0028280(412-424)Online publication date: 1991
https://doi.org/10.1007/BFb0028280
Bhattacharya BToussaint G(1991)Computing shortest transversalsComputing10.1007/BF0223916546:2(93-119)Online publication date: 5-Mar-1991
https://dl.acm.org/doi/10.1007/BF02239165

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