Visibility in geometry 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. (In the Earth's atmosphere light follows a slightly curved path that is not perfectly predictable, complicating the calculation of actual visibility.)
Computation of visibility is among the basic problems in computational geometry and has applications in computer graphics, motion planning, and other areas.
Concepts and problems
- Point visibility
- Edge visibility[1][2]
- Visibility polygon
- Weak visibility
- Art gallery problem or 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
- Painter's algorithm
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 0-521-87574-9.
Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (2000). Computational Geometry (2nd revised ed.). Springer-Verlag. ISBN 3-540-65620-0, 1st edition (1987): ISBN 3-540-61270-X. Chapter 15: "Visibility graphs"
D. Avis and G. T. Toussaint, "An optimal algorithm for determining the visibility of a polygon from an edge," IEEE Transactions on Computers, vol. C-30, No. 12, December 1981, pp. 910-914.
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
Undergraduate Texts in Mathematics
Graduate Studies in Mathematics
Hellenica World - Scientific Library
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