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Simple Characterization of LR-visibility Polygons

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Computational Geometry, Graphs and Applications (CGGA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7033))

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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.

Work by Tan was partially supported by Grant-in-Aid (23500024) for Scientific Research from Ministry of Education, Science and Culture, Japan, and Japan Society for the Promotion of Science.

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References

  1. Bhattacharya, B.K., Ghosh, S.K.: Characterizing LR-visibility polygons and related problems. Comput. Geom. Theory Appl. 18, 19–36 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. Heffernan, P.J.: An optimal algorithm for the two-guard problem. Int. J. Comput. Geom. Appl. 6(1), 15–44 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  3. Das, G., Heffernan, P.J., Narasimhan, G.: LR-visibility in polygons. Comput. Geom. Theory Appl. 7(1), 37–57 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ghosh, S.K.: Visibility problems in the plane. Cambridge University Press (2007)

    Google Scholar 

  5. Guibas, L., Hershberger, J., Leven, D., Sharir, M., Tarjan, R.: Linear time algorithms for visibility and shortest path problems inside triangulated simple polygons. Algorithmica 2, 209–233 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  6. Suzuki, I., Yamashita, M.: Searching for mobile intruders in a polygonal region. SIAM J. Comp. 21(5), 863–888 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  7. Tan, X.: A unified and efficient solution to the room search problem. Comput. Geom. Theory Appl. 40(1), 45–60 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Tseng, L.H., Heffernan, P.J., Lee, D.T.: Two-guard walkability of simple polygons. Int. J. Comput. Geom. Appl. 8(1), 85–116 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  9. O’Rourke, J.: Computational Geometry in C. Cambridge University Press (1993)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Science and Technology, Dalian Maritime University, Linghai Road 1, Dalian, China

    Xuehou Tan, Jing Zhang & Bo Jiang

  2. School of Information Science and Technology, Tokai University, 4-1-1 Kitakaname, Hiratsuka, 259-1292, Japan

    Xuehou Tan

Authors
  1. Xuehou Tan
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  2. Jing Zhang
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  3. Bo Jiang
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Editor information

Editors and Affiliations

  1. Research Institute of Education, Tokai University, 2-28-4 Tomigaya, Tokio, Shibuya-ku, Japan

    Jin Akiyama

  2. School of Computer Science and Technology, Dalian Maritime University, 116026, Dalian, China

    Jiang Bo

  3. Ibaraki University, Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Mikio Kano

  4. Tokai University, 4-1-1 Kitakaname, 259-1292, Hiratsuka, Japan

    Xuehou Tan

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© 2011 Springer-Verlag Berlin Heidelberg

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Tan, X., Zhang, J., Jiang, B. (2011). Simple Characterization of LR-visibility Polygons. In: Akiyama, J., Bo, J., Kano, M., Tan, X. (eds) Computational Geometry, Graphs and Applications. CGGA 2010. Lecture Notes in Computer Science, vol 7033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24983-9_18

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  • DOI: https://doi.org/10.1007/978-3-642-24983-9_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24982-2

  • Online ISBN: 978-3-642-24983-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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