THE POINT LOCATION PROBLEM IN CARTOGRAPHY

In this work, we focus on one of the most important problems in cartography applications, which is the point location (or polygon inclusion) problem. This problem is stated as follows: Assume that we have a polygon R and a query point P. We want to find out if the point P lies inside or outside the polygon R. Its solution depends on the shape of polygons and it can be easily solved for convex and star-shaped polygons. In the general case, the polygon should be split into smaller convex polygons and the problem is transformed into the problem ofpoint location in aplanar subdivision. The different algorithms, presented in international literature for the efficient solution of this problem are examined and compared. More precisely, we present the solution of Lee and Preparata, referred to the literature, as the nzethod of separating chains, as well as an invariant of this method, firstly introduced by Edelsbrunner, Guibas and Stolfi. The two methods will be presented in contrast to the method derived from the quadtrees of Samet and Webber. Moreover, our work is going to focus mainly on the method of Sarnak and Tarjan, which was based on the theory of persistence