# Visibility polygon

Visibility polygon

The visibility polygon or visibility region for a point "p" in the plane among non-transparent obstacles is the possibly unbounded polygonal region of all points of the plane visible from "p".

If the visibility polygon is bounded then it is a star-shaped polygon. This is the case, e.g., if the obstacles are the edges of a polygon and "p" is inside the polygon. In the latter case the visibility polygon may be found in linear time.cite book
author = Franco P. Preparata and Michael Ian Shamos | title = Computational Geometry - An Introduction | publisher = Springer-Verlag| year = 1985 | id = 1st edition: ISBN 0-387-96131-3; 2nd printing, corrected and expanded, 1988: ISBN 3-540-96131-3; Russian translation, 1989: ISBN 5-03-001041-6
]

Visibility polygons are studied in computational geometry and find their applications in motion planning.

oftware

* [http://www.VisiLibity.org VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types. This software can be used for calculating visibility polygons in polygonal environments with polygonal holes. A Matlab interface is also included.]

References

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