Characterizing and Recognizing Weak Visibility Polygons

A polygon is said to be a weak visibility polygon if every point of the polygon is visible from some point of an internal segment. In this paper we derive properties of shortest paths in weak visibility polygons and present a characterization of weak visibility polygons in terms of shortest paths between vertices. These properties lead to the following efficient algorithms: (i) an O(E) time algorithm for determining whether a simple polygon P is a weak visibility polygon and for computing a visibility chord if it exist, where E is the size of the visibility graph of P and (ii) an O(n2) time algorithm for computing the maximum hidden vertex set in an n-sided polygon weakly visible from a convex edge.

[1]  Tomás Lozano-Pérez,et al.  An algorithm for planning collision-free paths among polyhedral obstacles , 1979, CACM.

[2]  Joseph S. B. Mitchell,et al.  An Algorithmic Approach to Some Problems in Terrain Navigation , 1988, Artif. Intell..

[3]  Roman Kuc,et al.  Efficient representation of reflecting structures for a sonar navigation model , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[4]  Godfried T. Toussaint,et al.  Shortest path solves edge-to-edge visibility in a polygon , 1986, Pattern Recognit. Lett..

[5]  David Avis,et al.  A combinational approach to polygon similarity , 1983, IEEE Trans. Inf. Theory.

[6]  J. Ross Stenstrom,et al.  Building wire frames from multiple range views , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[7]  Bernard Chazelle,et al.  Triangulation and shape-complexity , 1984, TOGS.

[8]  Derek G. Corneil,et al.  Visibility graph recognition , 1990 .

[9]  Subhash Suri,et al.  An Optimal Algorithm for Detecting Weak Visibility of a Polygon , 1990, IEEE Trans. Computers.

[10]  Subir Kumar Ghosh.  Computing the Visibility Polygon from a Convex Set and Related Problems , 1991, J. Algorithms.

[11]  Willem F. Bronsvoort,et al.  Boundary evaluation and direct display of CSG models , 1988 .

[12]  Chong-Min Kyung,et al.  Hybrid shadow testing scheme for ray tracing , 1989 .

[13]  Michael McKenna.  Worst-case optimal hidden-surface removal , 1987, TOGS.

[14]  Sung Yong Shin,et al.  An optimal algorithm for finding all visible edges in a simple polygon , 1989, IEEE Trans. Robotics Autom..

[15]  G. G. Roy,et al.  SR: a PC-based CAD system for shadow and reflection studies in the built environment , 1989 .

[16]  Godfried T. Toussaint,et al.  An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge , 1981, IEEE Transactions on Computers.

[17]  Larry S. Davis,et al.  Computational Models of Space: Isovists and Isovist Fields , 1979 .