Fast and Robust Point-in-Spherical-Polygon Tests Using Multilevel Spherical Grids

Abstract

Point-in-spherical-polygon determination is widely required in applications over the earth. However, existing methods for point-in-polygon tests cannot be applied directly, due to non-Euclidean computation over the spherical surface. Thus, it is general to transform a spherical polygon into a planar polygon via projection, and then perform point-in-polygon tests. Unfortunately, this is expensive and may cause determination errors. In this paper, we propose to subdivide the spherical grid cells iteratively, and apply the ray-crossing method locally in grid cells, which is by one of our previous works. As a result, this not only avoids expensive transformation computation, but also guarantees robust determination for point-in-spherical-polygon tests. Experimental results attest our effectiveness, and show an acceleration of five orders of magnitude over a popularly used method.