Research On Representation, Computation And Reasoning Of 3D Topological Relationships

Spatial characteristics, attribute characteristics, time characteristics, and spatial relationships constitute the basic characteristics of spatial data. As the most important relationship of spatial relationships, topological relationships are constant relationship in the topological space transformation (translation, rotation, scaling).3D GIS is the future development trend of GIS.3D topological relationships are the research focus in 3D GIS. It has great theoretical and practical significance for study of 3D topological relationships.3D topological relationships play an important role in spatial data modeling, spatial query, spatial analysis, spatial data mining, and multiple representations of spatial data. But there are a number of problems in the research of 3D topological relationships. There is a contradiction between infinitely subdividing, more detail topological relationships and the limited knowledge. There are not three-dimensional topological relationships computing algorithms based on computational geometry algorithms. The research on 3D spatial reasoning is rarely. There are closely related among topological representation, computation and reasoning. So, we put emphasis on the above three aspects in this thesis. The main research content and results are as follows:(1) Considering the characteristics of spatial objects in 3D, a new data model called B-Rep-TIN-TEN is proposed based on the simplex theory in point set topology, ISO 19107 spatial schema and OpenGIS simple features specification. This spatial data model can express the geographical objects effectively.(2) A hierarchical representation method of topological relationships for 3D objects is proposed to solve the contradiction between the more detailed topological relations and the limited knowledge of people. Detail topological relationships can be represented by an integration framework composed of DE-9IM(Dimensionally Extended 9 Intersection Model) and SNE-9IM(Separation Number Extended 9 Intersection Model). We propose to group all detail cases into a few meaningful topological relationships as a basic topological relationships set. This can get a balance between detail topological relationships and basic topological relationships.(3) A new method for 3D topological relations calculation based on computational geometry algorithms is proposed. There are number of computational geometry algorithms including position judgment between point and linear object, position judgment between point and surface, position judgment between point and body, intersection computation between linear objects, intersection computation between linear object and surface, and intersection computation between surfaces are designed.3D topological relationships computing algorithms for spatial objects based on computational geometry algorithms are designed.(4) Based on B-Rep-TIN-TEN data model, we generalize 64 topological relationships reasoning among simple objects. The 64 topological relationships reasoning can be represented in combination table. Topological relationships reasoning among complex objects also set forth. Topological relationships reasoning knowledge database is constructed based on topological reasoning table which is used to reason. Topological relationship reasoning can promote the topological relationship calculation.(5) Based on the B-Rep-TIN-TEN data model, an experiment for the seamless integration of the aboveground, ground and underground objects is implemented. Some experiments for the topological relationships calculation and reasoning are conducted. A topological relationships calculation method based on reasoning is designed and the time efficiency is high. Those experiments verify the topological relationships representation, computation, and reasoning correctness.The proposed B-Rep-TIN-TEN data model integrates the merits of object-oriented data model and field data model and can express simple and complex objects. Topological relationships hierarchical representation method has solved the contradiction between infinitely subdividing, more detail topological relationships and the limited knowledge. The combination framework of DE-9IM and SNE-9IM can represent topological relationships completeness. The 9 basis topological relationships are more in line with human cognitive. The proposed topological relationships calculation methods effectively combine the computation geometry algorithms and can be used to compute the topological relationships. The proposed topological reasoning methods can accelerate the topological relationships computation.