Three dimensional weak visibility: Complexity and applications

  • Caoan Wang
  • Binhai Zhu
Session 2A: Computational Geometry
Part of the Lecture Notes in Computer Science book series (LNCS, volume 959)


In this paper, we study the complexity of 3D weak visibility. We obtain an O(n8) time and Θ(n6) 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(n6) time and O(n4) 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.


Visible Region Combinatorial Complexity Simple Polygon Polyhedral Surface Aspect Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Caoan Wang
    • 1
  • Binhai Zhu
    • 2
  1. 1.Dept. of Computer ScienceMemorial University of NewfoundlandCanada
  2. 2.Group C-3, MS M986Los Alamos National LaboratoryLos AlamosUSA

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