Skip to main content
Log in

The Superman problem

  • Published:
The Visual Computer Aims and scope Submit manuscript

Abstract

Given a polygonK contained in a polygonP, and a points lying outsideP, we present a Θ (n logn) algorithm that finds the minimum number of edges, ofP that we want to retain in order to hidek froms. Furthermore, if the visibility polygon ofs givenK is unbounded, the algorithm is shown to run in linear time. This paper is dedicated to J. Siegel and J. Shuster.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Asano T, Asano T (1983) Minimum partition of polygonal regions into trapezoids. In: Proceedings of the 24th Annual Symposium on the Foundations of Computer Science, Tucson, pp 233–241

  • Avis D, Toussaint G (1981) An optimal algorithm for determining the visibility of a polygon from an edge. IEEE Transactions on Computers C-30, pp 910–914

    Google Scholar 

  • Baumgart B (1972) Winged edge polyhedron representation. Stanford Artificial Intelligence, Report No. CS-320

  • Breen B (1977) L2 sets which are almost starshaped. Geom Dedic 6: 485–494

    Google Scholar 

  • Bruckner A, Bruckner J (1964) Generalized convex kernels. Israel J Math 2: 27–32

    Google Scholar 

  • Brown KG (1979) Geometric transformations for fast geometric algorithm. PhD Thesis, Department of Computer Science, Carnegie Mellon University

  • Chazelle B (1990) Triangulating a simple polygon in linear time. CS-TR-264-90, Princeton Univ

  • Chvátal V (1975) A combinatiorial theorem in plane geometry. J Combinat Theor Ser B 18: 38–41

    Google Scholar 

  • Dean, J, Lingas A, Sack J-R (1988) Recognizing polygons, or how to spy. Vis Comput 3: 344–355

    Google Scholar 

  • ElGindy H, Avis D (1981) A linear algorithm for computing the visibility polygon from a point. J Algorithms 2: 186–197

    Google Scholar 

  • Fournier A, Montuno D (1984) Triangulating simple polygons and equivalent problems. ACM Trans Graphics 3: 153–174

    Google Scholar 

  • Guibas L, Stolfi J (1985) Primitives for the manipulation of general subdivisions and the computations of Voronoi diagrans. ACM Trans on Graphics 4: 74–123

    Google Scholar 

  • Hanrahan P (1985) Topological shape models. PhD Thesis, University of Wisconsin-Madison

  • Hoffman K, Melhorn K, Rosenstiehl P, Tarjan R (1985) Sorting Jordan Sequences in linear time. In: Proc ACM symposium on Computational Geometry, Baltimore, pp 196–199

  • Horn A, Valentine F (1979) Some properties of L-sets in the plane. Duke Math J 16: 131–140

    Google Scholar 

  • Kay D, Gnay M (1970) Convexity and a certain propertyP m. Israel J Math 8: 39–52.

    Google Scholar 

  • Lee C, Lee D (1984) On a circle-cover minimization problem. Inf Process Lett 18: 109–115

    Google Scholar 

  • Lenhardt W, Pollack R, Sack J-R, Seidel R, Sharir, M, Suri S, Toussaint G, Whitesides S, Yap C (1987) Computing the link center of a simple polygon. In: Proceedings of the 3rd ACM Symposium on computational Geometry, Waterloo, pp 1–10

  • McCallum D, Avis D (1979) A linear algorithm for finding the convex hull of a simple polygon. Inf Process Lett 9: 201–206

    Google Scholar 

  • Motwani R, Raghunathan A, Saran H (1988) Covering orthogonal polygons with star polygons: the perfect graph approach. In: Proceedings of the 4th Annal ACM Symposium on Computational Geometry, Urbana-Champaign, pp 211–223

  • O'Rourke J (1987) Art gallery theorems and algorithms. Oxford University Press, Oxford

    Google Scholar 

  • Sack J, Suri S (1986) An optimal algorithm for detecting weak visibility of a polygon. Carleton University TR SCS-TR-114

  • Shermer T (1988) Link guarding simple polygons. McGill University TR SOCS-88.12

  • Suri S (1986) A linear time algorithm for minimum link paths inside a simple polygon. Comput Graphics Vis Image Process 35: 99–110

    Google Scholar 

  • Tarjan R, Wyk C van (1988) AnO (n log logn) algorithm for triangulating simple polygons. SIAM J Comput 17: 143–178

    Google Scholar 

  • Valentine F (1953) Minimal sets of Visibility Proceedings of the American Mathematical Soc 4: 917–921

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This work was supported by Friends of McGill Fellowship while T. Shemer was at McGill University.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mouawad, N., Shermer, T. The Superman problem. The Visual Computer 10, 459–473 (1994). https://doi.org/10.1007/BF01910636

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01910636

Key words

Navigation