visibility (geometry)
{{short description|Mathematical abstraction of objects being "visible"}}
In 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. (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 visibilityD. Avis and G. T. Toussaint, "[https://www.computer.org/csdl/trans/tc/1981/12/01675729-abs.html 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, "[https://mediatum.ub.tum.de/doc/1289339/file.pdf Sampling feature points for contour tracking with graphics hardware]", "In International Workshop on Vision, Modeling and Visualization (VMV)", Konstanz, Germany, October 2008.
- 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
- {{cite book
| first=Joseph
| last=O'Rourke
| authorlink = Joseph O'Rourke (professor)
| year=1987
| title=Art Gallery Theorems and Algorithms
| title-link=Art Gallery Theorems and Algorithms
| publisher= Oxford University Press
| isbn=0-19-503965-3
}}
- {{cite book
| first=Subir Kumar
| last=Ghosh
| year=2007
| title=Visibility Algorithms in the Plane
| publisher=Cambridge University Press
| isbn=978-0-521-87574-5
}}
- {{cite book
|author = Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf | year = 2000 | title = Computational Geometry | publisher = Springer-Verlag | isbn = 3-540-65620-0 | edition = 2nd revised | id = 1st edition (1987)}} Chapter 15: "Visibility graphs"
External links
=Software=
- [http://www.VisiLibity.org VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types]
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