On the complexity of point-in-polygon algorithms

Point-in-polygon is one of the fundamental operations of Geographic Information Systems. A number of algorithms can be applied. Different algorithms lead to different running efficiencies. In the study, the complexities of eight point-in-polygon algorithms were analyzed. General and specific examples are studied. In the general example, an unlimited number of nodes are assumed; whereas in the second example, eight nodes are specified. For convex polygons, the sum of area method, the sign of offset method, and the orientation method is well suited for a single point query. For possibly concave polygons, the ray intersection method and the swath method should be selected. For eight node polygons, the ray intersection method with bounding rectangles is faster.