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Optimal Algorithms for the Set Operations of Two Visibility Polygons in a Simple Polygon  

김수환 (부산외국어대학교 컴퓨터공학부)
Publication Information
Journal of KIISE:Computer Systems and Theory / v.31, no.1_2, 2004 , pp. 102-111 More about this Journal
Abstract
The visibility polygon of a simple polygon P is the set of points which are visible from a visibility source in P such as a point or an edge. Since a visibility polygon is the set of points, the set operations such as intersection, union, or difference can be executed on them. The intersection (resp. union) of two visibility polygons is the set of points which are visible from both (resp. either) of the corresponding two visibility sources. The difference of two visibility polygons is the set of points which are visible from only a visibility source. Previously, the best known algorithm for the set operations of two polygons with total n vertices takes O(nlogn ＋ k) time, where k is the output size. In this paper, we present O(n) time algorithms for computing the intersection, the union, and the difference of given two visibility polygons, which are optimal.
Keywords
Visibility; Visibility Polygon; Art Gallery Problem; Optimal Algorithms;
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1 H. G. Mairson and J. Stolfi, 'Reporting and counting intersections in the plane,' Tech Rep., Dept. of Computer Science, Stanford University, 1983
2 E. ElGindy, D. Avis, and G. T. Toussaint, 'A linear algorithm for computing the visibility polygon from a point,' J. Algorithms, Vol. 2, pp. 190-197, 1981
3 D. T. Lee, 'Visibility of a simple polygon,' Computer Vision, Graphics, and Image Processing, Vol. 22, pp. 207 -221, 1983   DOI
4 D. Avis and G. T. Toussaint, 'an optimal algorithm for determining the visibility from an edge,' The Visual Computer, Vol. 2, pp. 342-357, 1986   DOI
5 G. T. Toussaint, 'A linear time algorithm for solving the strong hidden line problem in a simple polygon,' Pattern Recognition Letters, Vol. 4, pp. 449-451, 1986   DOI   ScienceOn
6 L. Guibas, J. Hershberger, D. Leven, M. Shri r, and R. E. Tarjan, 'Linear time algorithm for visibility and shortest path problems inside triangulated simple polygons,' Algorithrnica, Vol. 2, pp. 209-233, 1987   DOI
7 P. J. Heffernan and S. B. Mitchell, 'Structured visibility profiles with applications to problems in simple polygons,' Proc. 16th Annual Syrnp. on Comput. Geometry, pp. 53-62, 1990
8 S. H. Kim and K. Y. Chwa, 'An optimal algorithm for computing the edge visibility polygon from an edge of a simple polygon,' Proc. of KISS ConI., Vol. 17, No.2, pp. 769-772, 1990
9 J. O'Rourke, Art Gallery Theorems and Algorithms, Oxford University Press, 1987
10 M. Mckenna, 'Worst-case optimal hidden-surface removal,' ACM Tr. on Graphics, Vol. 6, pp. 1928, 1987   DOI   ScienceOn
11 S. S. Ahn, 'Output Sensitive Polygon Intersection,' MS thesis, KAIST, Korea, 1991
12 F. D. Prepatata and M. I. Shamos, Computational Geometry: An Introduction, Springer-Verlag, 1985
13 G. T. Toussaint, 'A simple linear algorithm for intersecting convex polygons,' The Visual Computer, Vol. 1, pp. 118-123, 1985   DOI