Visibility (geometry)

Visibility is a mathematical abstraction of the real-life notion of visibility.

Given a set of obstacles in the Euclidean space, two points in the space are said to be visible to each other, if the line segment that joins them does not intersect any obstacles.

Computation of visibility is among the basic problems in computational geometry and finds applications in computer graphics, motion planning, and other areas.

Notions and problems

• Point visibility
• Edge visibility^[1][2]
• Visibility polygon
• Weak visibility
• Art gallery problem (The museum problem)
• Visibility graph
  • Visibility graph of vertical line segments
• Watchman route problem
• Computer graphics applications:
  • Hidden surface determination
  • Hidden line removal
  • z-buffering
  • portal engine
• Star-shaped polygon
  • Kernel of a polygon
• Isovist
• Viewshed
• Zone of Visual Influence

References

• O'Rourke, Joseph (1987). Art Gallery Theorems and Algorithms. Oxford University Press. ISBN 0-19-503965-3. 
• Ghosh, Subir Kumar (2007). Visibility Algorithms in the Plane. Cambridge University Press. ISBN 0521875749. 
• Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000). Computational Geometry (2nd revised edition ed.). Springer-Verlag. ISBN 3-540-65620-0, 1st edition (1987): ISBN 3-540-61270-X.  Chapter 15: "Visibility graphs"

1. ^ D. Avis and G. T. Toussaint, "An optimal algorithm for determining the visibility of a polygon from an edge," IEEE Transactions Computers, vol. C-30, No. 12, December 1981, pp. 910-914.
2. ^ E. Roth, G. Panin and A. Knoll, "Sampling feature points for contour tracking with graphics hardware", "In International Workshop on Vision, Modeling and Visualization (VMV)", Konstanz, Germany, October 2008.

External links

Software

• VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types