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Antonio Lopez Lopez

Fernando Sainz-Ezquerra Dominguez


The origin of this paper is the following:
In a Spanish province there was an electric network composed essentially by transformation centers and flowlines that joined them together. The geometric representation in the Cartesian plane is a closed polygon, (smashed in general). The towns inside the polygon receive energy from the network, those outside it do not. When any center or line has a failure, it is necessary to repair the electric network as soon as possible. Then, the polygon is changed and some areas can alter their electric supply from the network because they may have changed their situation in relation to the polygon. To decide about the position of each location force us to study the problem of the position of a point, in the plane, in relation to a polygon.
Of course, we knew that there was a solution to this problem, in addition we had applied the suitable program. But, in particular, when a lot of vertices of the polygon (the transformation centers), are very close to each other and, at the same time, our point in study (the town about which we want to decide), is also close to these vertices, the program did not always finish correctly or, even worse, it gave us a false answer. This is why we no longer use this solution to the problem and we have found the following one.

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