A convex polygon, for example, can always be guarded with one camera. But even when two polygons have the same number of vertices, one can be easier to guard than the other. We shall therefore express the bound on the number of cameras needed in terms of n, the number of vertices of the polygon. How many cameras do we need to guard a simple polygon? This clearly depends on the polygon at hand: the more complex the polygon, the more cameras are required. A camera sees those points in the polygon to which it can be connected with an open segment that lies in the interior of the polygon. A camera position in the gallery corresponds to a point in the polygon. We further restrict ourselves to regions that are simple polygons, that is, regions enclosed by a single closed polygonal chain that does not intersect itself. Therefore we model a gallery as a polygonal region in the plane. A gallery is, of course, a 3-dimensional space, but a floor plan gives us enough information to place the cameras. If we want to define the art gallery problem more precisely, we should first formalize the notion of gallery. Referred to as the Art Gallery Problem: how many cameras do we need to guardĪ given gallery and how do we decide where to place them? So we should place the cameras at strategic positions, such thatĮach of them guards a large part of the gallery. Too few cameras, because every part of the gallery must be visible to at least An additional advantage of a small number of cameras is that theĬost of the security system will be lower.
#How to turn a polygon into a line transcad tv#
Because it is easier to keep an eye onįew TV screens rather than on many, the number of cameras should be as smallĪs possible. The images from the cameras are sent to TV These cameras are usually hung from the ceiling and Art galleries therefore have to guard their collections carefully.ĭuring the day the attendants can keep a look-out, but at night this has to beĭone by video cameras. They are very valuable, easy to transport, and apparently not so difficult to sell. Works of famous painters are not only popular among art lovers, but also among criminals.
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