Editing Art gallery problem (section)

{{Short description|Mathematical problem}}
The '''art gallery problem''' or '''museum problem''' is a well-studied [[visibility problem]] in [[computational geometry]].  It originates from the following real-world problem:

<blockquote> "In an [[art gallery]], what is the minimum number of guards who together can observe the whole gallery?" </blockquote>

In the geometric version of the problem, the layout of the art gallery is represented by a [[simple polygon]] and each guard is represented by a [[point (geometry)|point]] in the polygon.  A set <math>S</math> of points is said to guard a polygon if, for every point <math>p</math> in the polygon, there is some <math>q\in S</math> such that the [[line segment]] between <math>p</math> and <math>q</math> does not leave the polygon.

The art gallery problem can be applied in several domains such as in [[robotics]], when [[Artificial intelligence|artificial intelligences (AI)]] need to execute movements depending on their surroundings. Other domains, where this problem is applied, are in [[image editing]], lighting problems of a stage or installation of infrastructures for the warning of natural disasters.