Research On Key Techniques Of 3D Spatial Topological Analysis

With the development of the applications such as military, mining and transportation, the demand of 3D spatial applications is increasingly high. The topological relations between 3D spatial objects reflect the topological invariant of the topological transferlaiton 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 pratical applications.The paper is concerned with the problem that the typical 3D spatial data models can not support the 3D spatial analysis well. The systemica research of the 3D spatial topological analysis is taken from the aspects of 3D spatial data model, 3D topological reasoning, 3D spatial data structure and 3D spatial operations. The main contributions of this paper can be included as follows:Firstly, a 3D spatial data model named 3DRDM (3D realms data model)is proposed. The model is constructed based on the 3D discrete domain named 3D realms, which can be divided by four layers: 3D geometric primitives layer, 3D discrete domain layer, basic construction element layer and basic spatial object layer. The topogical correctness can be proved by the constraints of the 3D realms. The spatial data model can represent rather compicated 3D spatial objects and has advantages of the more powerful representation abilidy and the support the 3D spatial topological analysis.Secondly, the completeness of the possible topological relations between the 3D basic objects has been proved. 69 negative conditions of the 3D basic spatial objects are proposed and proved. The impossible topological relations are excluded by these negative conditions, then the possible topological relations remain. Each possible relation is illustrated and the completeness between the basic spatial objects is proved.Thirdly, the analysis algorithms between the compound 3D spatial objects are presented. Using the completeness of the 3D basic spatial objects and the method of compound reasoning, the algorithm of the topological analysis between the compound line and body object based on the topological relations between basic line and basic body is presented; the algorithms of the topological analysis between compound body objects based on the basic body objects are presented. The correctness of all the algorithms has been proved and the completeness of the topological relations between compound objects is also analyzed.Finally, the 3D spatial data model and the related algorithm are proposed. The notation of dual grid is proposed to prove the correctness of the 3D topolocal analysis. Then a 3D spatial data structure is proposed. It can represent the 3D spatial object well and support the related 3D spatial operations well. The 3D spatial operations which can be divided into numeric operations, topological operatioans and spatial objects operations are proposed to implement. The topological algorithms between the point and body, body and body are introduced as the examples.