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

Star-shaped polygon

A star-shaped polygon is a polygonal region in the plane which is a star domain, i.e., a polygon P is star-shaped, if there exists a point z such that for each point p of P the segment zp lies entirely within P.The set of all points z with the described property is called the kernel of...

. 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.

Visibility polygons are studied in computational geometry

Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry. Some purely geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational...

 and find their applications in motion planning

Motion planning

Motion planning is a term used in robotics for the process of detailing a task into discrete motions....

.

External links

• visibility in simple polygons - applets

Software

• VisiLibity: A free open source C++ library of floating-point visibility algorithms and supporting data types, calculates visibility polygons in polygonal environments with polygonal holes