A point in non-convex polygon location problem using the polar space subdivision in E2

Abstract

The point inside/outside a polygon test is used by many applications in computer graphics, computer games and geographical information systems. When this test is repeated several times with the same polygon a data structure is necessary in order to reduce the linear time needed to obtain an inclusion result. In the literature, different approaches, like grids or quadtrees, have been proposed for reducing the complexity of these algorithms. We propose a new method using a polar space subdivision to reduce the time necessary for this inclusion test. The proposed algorithm is robust and has a performance of O(k), where k ≪ N, k is the number of tested intersections with polygon edges, and the time complexity of the preprocessing is O(N), where N is the number of polygon edges.