Simple characterization of LR-visibility polygons

Authors:
Xuehou Tan;Jing Zhang;Bo Jiang
Affiliations:
School of Information Science and Technology, Dalian Maritime University, Dalian, China;School of Information Science and Technology, Dalian Maritime University, Dalian, China;School of Information Science and Technology, Dalian Maritime University, Dalian, China
Venue:
CGGA'10 Proceedings of the 9th international conference on Computational Geometry, Graphs and Applications
Year:
2010

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Abstract

A simple polygon P is LR-visible if there are two points s, t on the boundary of P such that every point on the clockwise boundary of P from s to t is visible from some point of the other boundary of P from t to s and visa versa. In this paper, we give a simple, explict characterization of LR-visibility polygons. It is obtained by mapping the structure of non-redundant components used in determining LR-visibility into a set of directed chords of a circle. Using our characterization, we further develop a simple O(n) time algorithm for determining whether a given polygon is LR-visible. This greatly simplifies the existing algorithms for determining whether a simple polygon is LR-visible and for reporting all pairs s and t which admit LR-visibility as well.