Research on 3D Geographic Fence Algorithm Based on Linear Equation

Abstract

Three-dimensional spatial geo-fencing is a new application based on location-based services (LBS, Location Based Services), which can provide real-time, three-dimensional location change-based related services to fence associates, and its core is to judge the location relationship between target points and fence area, which can be abstracted as point and space figure location relationship discrimination in geometry and mathematics, i.e., point inclusion problem. At present, the mainstream ray method has singularity problem in boundary judgment, and although many improved algorithms have been proposed, most of them are limited to two-dimensional form, which cannot meet the demand of high-precision position discrimination for complex spatial three-dimensional environment. Therefore, this paper starts from the idea of solving a system of linear equations, transforms the judgment of the position relationship between points and polyhedral fences into the judgment of the position relationship between points and planes, and proposes a new algorithm of 3D geo-fencing based on linear equations, which can quickly and accurately complete the judgment of the position relationship between target points and fences. Firstly, the complex polyhedral fence is pre-processed and formed into a binary tree by combining the idea of convex dissection and BSP tree technology; secondly, the target point is recursively queried to be located in the binary tree and the sub-convex polyhedral fence data is obtained; finally, the linear equation algorithm is used to judge the point inclusion between the target point and the sub-convex polyhedron. Experimental results show that the new linear equation algorithm is 40%-48.49% more efficient in convex polyhedral fence position discrimination and 12.5%-20% more efficient in simple nonconvex polyhedral fences compared with the improved ray method.