Simplex-based 3D Spatial Objects Embedded Data Model And Computation Of Topological Relations

The topological relations between 3D spatial objects reflect the topological invariant of the topological transformation which includes translation, zooming and rotation. The topological relation is the most basic spatial relation and shows the inner relation between the spatial objects which are independent with the geometric deformation. They are very important in practical applications. Currently,9-intersection method is most popular to be used for the studies and applications of topological relations in GIS. However, previous studies focused on the representation and reasoning of spatial relations in the two dimensional space. Progress on similar studies combined with data model in the three-dimensional space has been very limited. To improve the current methods and models for spatial relations, this paper research on this key issue.Based on the analysis of existing three-dimensional spatial data model and the simplex theory, a new 3D spatial data model, called simplex-based object embedded data model is presented. This model depends on tetrahedral mesh, the simplexes are the basic geometric elements, all 3D spatial objects (simple or complicated) are expressed by a set of simplexes. In this thesis, the expression of spatial objects and spatial data structure are described in detail, and also explores the process of building three-dimensional spatial field, the basic operations and etc. As the model has both the characteristics of the feature model and field model, it has advantages of the more powerful representation ability and support 3D spatial topological analysis.After the study of 3D spatial data model, the paper also proposes a simplicial complex-based topological relations model which is simply called SCTRM to describe the 3D topological relations. By calculating the intersection of two simplexes'sets, that can easily distinguish the topological relations of two 3D spatial objects. In theory, this model can not only describe the most types of topological relations, but also can expressed in a much detailed way than the traditional topological models. Overall, this approach is with strong comprehensiveness, computability and operability, so can overcome the short comings of existing methods and presents a new idea for computing different spatial relations.Using SCTRM, according to the principle of modular design and the strategy of gradual optimization, the methods of calculating topological relations are designed. Every algorithm is described with the flow chart. Combined with the expression of three-dimensional solid model and spatial data storage, construction and management of spatial field, the visualization of three-dimensional entity and calculation of topological relations are achieved. A prototype system is developed independently to examine the new method and models using C++on the platform of Windows XP. Experimental results with the practical and simulated spatial data show the reasonability and practicability of the new method. Thus we provide a complete solution of 3D topological relations from theoretical model to the methods of calculating. It is also useful for spatial query and spatial analysis.