The Topological Relations’ Description Of Simple Body Entities Based On Euler Number

ABSTRACT:3D Spatial Relationship is a key issue in3D GIS research field.It includes three main aspects:metric relation, order relation and topological relation, they are the theoretical basis of data representing, searching, analyzing and applying in3D space. Among them, topological relation is the most important relation.3D topological relations mainly study the topological invariant of the topological transformation (translation, zoom, rotation). Currently, the academic authorities’studies and analysis mainly focus on the decomposition-based models, but some problems exist on these models such as inconsistent topological definition, weak distinguishing ability, and lacking of hierarchy description manner. Consider the existing research and the2D topological relation model based on whole-based idea, this paper mainly discusses the distinction and description of topological relations between simple body entities in the3D space. The principal research work and innovations are listed as follows:(1) Based on the manifold topology theory, four kind of spatial entities in the3D space are defined:including point, line, surface and body. The geometric structure and internal relationship of these entities are described.(2) According to the existing topology theory, the calculating method of Euler number of four kind of spatial entities in3D space is analyzed, and the topological relation model based on Euler number in2D space is extended to the3D space. Therefore, a3D topological relation model based on the Euler number is formed, which provides a new theoretical framework for the analysis and description of the topological relations on3D spatial entities.(3) The calculating method of the connected component numbers after the operation of intersecting and differential are defined, and nearly30kinds of topological relationships between simple body are described by the hierarchy description model based on the Euler number; Compared with 9I model and its developed models, the advantage of the hierarchy description model based on Euler number is described. This model provides the theoretical foundation for the description and calculation of topological relationships between various entities in3D space.