Efficient Point-in-Polygon Tests by Grids Without the Trouble of Tuning the Grid Resolutions

The grid-based approach is popular for point-in-polygon tests. However, there is a trade-off between the preprocessing and the inclusion test, which always requires the grid resolutions to be tuned. In this article, we address this challenge by enhancing the grid structure using y-axis-aligned stripes, which are formed by the y-axis-aligned lines passing through the endpoints of the edge segments in the cell, thereby managing the edge segments in each grid cell. Moreover, we precompute the inclusion properties of the x-axis-aligned top borders of the stripes during preprocessing. Therefore, to answer a query point with the ray crossing method, we can emit a ray from the point to propagate upwards until the ray arrives at the top border of a stripe. We thoroughly consider singular cases to guarantee each query point can be answered in the stripe that contains the point. In our method, the computational load can be decreased, as one coordinate of the intersection point between the ray and an edge is known in advance, and parallel computing can be well exploited because the branching operations for determining whether an edge intersects with the ray are saved. Experimental results show that the efficiency of our method does not vary much with respect to the grid resolutions, so the trouble of tuning grid resolutions can be avoided. Ultimately, our method with a low grid resolution can reduce the preprocessing time and still achieve a higher inclusion test efficiency than the existing methods with a high grid resolution, especially on GPUs.