Abstract
To computer circular visibility inside a simple polygon, circular arcs that emanate from a given interior point are classified with respect to the edges of the polygon they first intersect. Representing these sets of circular arcs by their centers results in a planar partition called the circular visibility diagram. AnO(n) algorithm is given for constructing the circular visibility diagram for a simple polygon withn vertices.
Similar content being viewed by others
References
Agarwal, P. K., and M. Sharir, Circular visibility from a point in a simple polygon,Internat. J. Comput. Geom. Appl.,3(1), 1–25, 1993.
Agarwal, P. K., and M. Sharir, Circle shooting in a simple polygon,J. Algorithms,14, 69–87, 1993.
Avis, D., and G. T. Toussaint, An optimal algorithm for determining the visibility of a polygon from an edge,IEEE Trans. Comput.,30, 910–914, 1981.
Baker, W. M.,Algebraic Geometry: A New Treatise on Analytical Conic Sections, Bell, London, 1906.
Chazelle, B. M., Triangulating a simply polygon in linear time,Discrete Computat. Geom.,6, 485–524, 1991.
Chazelle, B. M., and L. T. Guibas, Visibility and intersection problems in plane geometry,Discrete Comput. Geom.,4, 551–581, 1989.
Chazelle, B. M., L. T. Guibas, and D. T. Lee, The power of geometric duality,BIT,25(1), 76–90, 1985.
Chou, S. Y., L. L. Chen, and T. C. Woo, Circular Visibility of a Simple Polygon, Working Paper 92-102, Department of Industrial and Manufacturing Systems Engineering, Iowa State University, 1992.
Chou, S. Y., L. L. Chen, and T. C. Woo, Parabolic Visibility in the Plane, Working Paper 92-103, Department of Industrial and Manufacturing Systems Engineering, Iowa State University, 1992.
Edelsbrunner, H.,Algorithms in Combinatorial Geometry, Springer-Verlag, New York, 1987.
Edelsbrunner, H., and L. J. Guibas, Topologically sweeping an arrangement,J. Comput. System Sci 38 165–194, 1989.
Guibas, L., J. Hershberger, D. Leven, M. Sharir, and R. Tarjan, Linear-time visibility and shortest path problems inside triangulated simple polygons,Algorithmica,2, 209–233, 1987.
Joe, B., and R. B. Simpson, Correction to Lee's visibility polygon algorithm,BIT 27 458–473, 1987.
Lee, D. T., Visibility of a simple polygon,Comput. Vision Graphics Image process.,22, 207–221, 1983.
Lee, D. T., and Y. T. Ching, The power of geometric duality revisited,Inform. Process, Lett.,21, 117–122, 1985.
Lee, D. T., and F. P. Preparata, An optimal algorithm for finding the kernel of a polygon,J. Assoc. Comput. Mach.,26, 415–421, 1979.
O'Rourke, J.,Art Gallery Theorems and Algorithms, Oxford University Press, Oxford, 1987.
Preparata, F., and M. I. Shamos,Computational Geometry: An Introduction, Springer-Verlag, New York, 1985.
Suri, S., A linear time algorithm for minimum link paths inside a simply polygon,Comput. Vision Graphics Image Process.,35, 99–110, 1986.
Suri, S., and J. O'Rourke, Worst-case optimal algorithms for constructing visibility polygons with holes,Proc. 2nd ACM Symp. on Computational Geometry, Yorktown Heights, NY, 1986, pp. 14–23.
Tarjan, R. E., and C. van Wyk, AnO(n) log log n-time algorithm for triangulating a simple polygon,SIAM J. Comput.,17(5), 143–178, 1985.
Author information
Authors and Affiliations
Additional information
Communicated by D. T. Lee.
Rights and permissions
About this article
Cite this article
Chou, SY., Woo, T.C. A linear-time algorithm for constructing a circular visibility diagram. Algorithmica 14, 203–228 (1995). https://doi.org/10.1007/BF01206329
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01206329