Boundary restricted non-overlapping sphere tree for unified multidimensional solid object index

Abstract

To solve leakages as complex subdivision structures, high nodes overlap probability and poor supporting on multi-dimensional entity object retrievals and the computation of existing spatial indexes. This paper presents a boundary restricted non-overlapping sphere tree for a unified multidimensional solid object index. By using the outer product expression of a sphere in Geometric Algebra, an approach is explored for intersection judgments and point extractions between lines and planes and lines and spherical surfaces based on meet operators. The element subdivision of multi-dimensional object voxelization and the boundary restricted non-overlapping sphere-filling algorithm is developed to balance the conditions (e.g. granularity, non-overlapping subdivision of object voxelization), the duplication and approximate degrees of approaching objects. Furthermore, generating and updating minimum boundary sphere and batch Neural Gas hierarchical clustering algorithm is also presented, and contains a volume adjusted, index level system steady with the balance of each branch of a sphere tree. Next, with the advantage of a clear geometric meaning, simple geometric relations calculation among spheres and dynamical updateable parameters, index structure can be dynamically generated and updated. Finally, the unified multidimensional solid object index, a query mechanism of any location and range on and in the solid objects is proposed. The updated minimum boundary sphere construction, algorithm, and the volume adjusted adaptive batch Neural Gas hierarchical cluster algorithm are defined to quickly, robustly, relatively, and uniformly classify the filling sphere. The simulation of different physical objects and performance comparison with a commonly used sphere tree indexes suggest that the proposed index can effectively query any position or regions on and in the solid objects, and support the nearest linkage distance and dynamical overlapping query under limited time restrictions with high precision. © 2012 ISCAS.