Hexagon-based adaptive hierarchies for efficient point-in-spherical-polygon tests on GPUs

Abstract

Point-in-spherical-polygon tests are a fundamental problem in computational geometry. For such tests, efficiency is much required for many global information processing matters, especially their real-time processing. Though many efforts have been made, it is still challenging due to the constraints from the non-Euclidean space of the sphere. Recently, a method is proposed to construct an Adaptive Hexagonal Hierarchical Grid (AHHG) to manage spherical polygon edges, by which the non-Euclidean space constraint of the sphere can be well handled to improve point-in-spherical-polygon tests. However, this method is very expensive in the construction of AHHGs, which prevents its use in practice. In this paper, we present novel measures to divide the task of AHHG construction into several subtasks to solve the problems that arise in the parallel construction of incongruent adaptive hierarchies, so we can exploit the parallel computing potential of GPUs for acceleration. We also develop measures to adaptively optimize the hierarchical levels of an AHHG for high efficiency. Experimental results show that we can answer 1,000,000 query points against dynamically varying spherical polygons in over 100,000 edges in real time on a personnel computer, where AHHGs for spherical polygons are individually constructed. This is much superior to the existing methods.