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Three dimensional weak visibility: Complexity and applications

  • Session 2A: Computational Geometry
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

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Abstract

In this paper, we study the complexity of 3D weak visibility. We obtain an O(n 8) time and Θ(n 6) space algorithm to compute the weakly visible region of a triangle F from another triangle G among general scenes, which are a set of n disjoint triangles. We also consider the cases when the scenes are rectilinear objects and polyhedral terrains. We show that in these special situations the weakly visible regions can be computed much faster in O(n 6) time and O(n 4) space. With these results, we obtain the first known polynomial time algorithm to decide whether or not a simple polyhedron is weakly (internally or externally) visible.

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Author information

Authors and Affiliations

  1. Dept. of Computer Science, Memorial University of Newfoundland, Canada

    Caoan Wang

  2. Group C-3, MS M986, Los Alamos National Laboratory, Los Alamos, NM, USA

    Binhai Zhu

Authors
  1. Caoan Wang
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  2. Binhai Zhu
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Ding-Zhu Du Ming Li

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© 1995 Springer-Verlag Berlin Heidelberg

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Wang, C., Zhu, B. (1995). Three dimensional weak visibility: Complexity and applications. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030819

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  • DOI: https://doi.org/10.1007/BFb0030819

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

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