Fast and robust GPU-based point-in-polyhedron determination

This paper presents a fast and robust GPU-based point-in-polyhedron determination method. The method partitions the bounding box of the polyhedron into a grid with O(N) cells, where N is the number of polyhedron faces, and predetermines the inclusion property of the grid cells' center points. Then, a line segment is generated from the query point to the center point of its related grid cell to determine the inclusion property of the query point by counting the faces intersected by the line segment. Such a localization treatment is further exploited to optimize the visiting pattern in using GPUs, by which a high increase in the testing speed is achieved. We also provide a unified solution to all singular cases, especially those caused by localization, to guarantee the efficiency and robustness for point-in-polyhedron tests. The results show that our proposed method can be faster than both state-of-the-art serial and parallel methods by several orders of magnitude, with only a slight increase in storage requirement.