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.

中文翻译：

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通过网格进行高效的多边形内点测试，无需调整网格分辨率


基于网格的方法在多边形点测试中很流行。然而，预处理和包含测试之间存在权衡，这总是需要调整网格分辨率。在本文中，我们通过使用 y 轴对齐条纹增强网格结构来解决这一挑战，这些条纹由穿过单元格中边缘段端点的 y 轴对齐线形成，从而管理每个网格单元。此外，我们在预处理过程中预先计算了条纹的 x 轴对齐顶部边框的包含属性。因此，为了用射线交叉方法回答查询点，我们可以从该点发射一条射线向上传播，直到射线到达条带的上边界。我们彻底考虑奇异情况，以保证每个查询点都可以在包含该点的条带中得到回答。在我们的方法中，由于预先知道射线与边缘之间的交点的一个坐标，因此可以减少计算量，并且可以很好地利用并行计算，因为确定边缘是否与射线相交的分支操作是已保存。实验结果表明，我们的方法的效率随网格分辨率变化不大，因此可以避免调整网格分辨率的麻烦。最终，我们的低网格分辨率方法可以减少预处理时间，并且仍然比现有的高网格分辨率方法实现更高的包含测试效率，尤其是在 GPU 上。