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Visibility polygon : ウィキペディア英語版
Visibility polygon

In computational geometry, the visibility polygon or visibility region for a point ''p'' in the plane among obstacles is the possibly unbounded polygonal region of all points of the plane visible from ''p''. The visibility polygon can also be defined for visibility from a segment, or a polygon. Visibility polygons are useful in robotics, video games, and in determining positions to locate facilities, such as the best placement of security guards in an art gallery.
If the visibility polygon is bounded then it is a star-shaped polygon. A visibility polygon is bounded if all rays shooting from the point eventually terminate in some obstacle. This is the case, e.g., if the obstacles are the edges of a simple polygon and ''p'' is inside the polygon. In the latter case the visibility polygon may be found in linear time.

== Definitions ==
Formally, we can define the planar visibility polygon problem as such. Let S be a set of obstacles (either segments, or polygons) in \mathbb^2. Let p be a point in \mathbb^2 that is not within an obstacle. Then, the ''point visibility polygon'' V is the set of points in \mathbb^2, such that for every point q in V, the segment pq does not intersect any obstacle in S.
Likewise, the ''segment visibility polygon'' or ''edge visibility polygon'' is the portion visible to any point along a line segment.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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