The Expression Of Topological Relations Between3D Objects With Holes

At present, the geographic information system is widely applied in many fields, whilespatial analysis also becomes the research hot spot as its important symbol that distinguish fromother information system. Of which the topological relations is the basal study of the spatialanalysis, its related theory and technology have been relatively mature. But the current researchabout the topological relation mostly confined to the two-dimensional space, several topologicalmodel that is widely used can express the topological relations better which are between simpleobjects or objects with holes in the two-dimensional space. But there is less study for thetopological relations between spatial objects or objects with holes in the three-dimensional space.In this paper, we study the representation and reasoning of the topological relations betweenobjects in the three-dimensional space on the basis of the existing theory.The main work of this paper includes:(1) It introduces the background and significance ofthe research research in this paper, and analyzes the current status of the research that thetopological relations between spatial objects. Then it mainly introduces several kinds of currentwidely used topological model，such as：4-intersection model、9-intersection model、TRCRmodel、9+-intersection model、D9-intersection mode and so on. And at the same time comparesthe advantages and disadvantages of each model.(2) This paper introduces the theoretical basisthat the study of this paper based on, including some basic definitions of point-set topologytheory, n-intersection model, the results of predecessors researching for the topological relationsbetween spatial objects with holes in two-dimensional spatial. Then it analyzes the possibilityand limitations that TRCR model and9+-intersection model are applied to research thetopological relations between objects with holes in three-dimensional space.(3)3D9-intersection model is proposed based on n-intersection model which can express thetopological relations between simple objects in three-dimensional space. It can distinguish14kinds of topological relations between simple objects in the three dimensional space by usingthis model. According to analysis and comparison of the expression ability between this modeland the9-intersection model, we sums up the advantages of the expressing power that3D9-intersection model has, and then gives the conceptual neighborhood graphs of the topologicalrelations between simple objects in three-dimensional space and its possible topological relationsof combinatorial reasoning. It is the foundation for the spatial reason of the topological relationsbetween spatial objects with holes in three-dimensional space.(4) Combining the advantages of TRCR model that put forward by Climentini and the9+-intersection model that put forward byYohei Kurata, and at the same time introducing the thought of dimension widening, we putforward the3D9+-intersection model to express the topological relations between3d spasialobjects with holes. Then this paper sums up58kinds of topological relations between the threedimensional spatial object with hole (limiting with only one hole) and the three dimensionalsimple object, and682kinds of topological relations between two3d spatial objects with hole(limiting with only one hole), and at the same time gives the conceptual neighborhood graphs. Inthe last part of the paper, it is explained that this model can also express the topological relationsbetween spatial objects with multiple holes by illustrating an instance.(5) It lists severalexamples, such as: the groundwater contaminant source, the mining in mine field and theproperty rights of underground parking, and then it illustrates the application significance of3D9+-intersection model in the real world. Then it abstracts the objects in the real world, such as theunderground water, the mining in mine and underground parking into the spatial objects withholes in three-dimensional space. And then respectively studies how to use the3D9+-intersection model to study the finding of the groundwater contaminant source, the line ofmining in mine, the partition of underground parking lot. Then it lists some simple examples, andusing the model to analyze the topological relations of spatial objects with holes in the threedimensional space respectively between points, lines, simple bodies. In the last it illustrates thepractical significance of the model.In this paper, the3D9-intersection model which considering the thought of dimensionwidening on the basis of9-intersection model, and its expression ability enhances greatly, whichis more suitable for expressing the topological relations between objects in the three-dimensionalspace. And the3D9+-intersection model proposed in this paper which can express thetopological relations between objects with holes in the three-dimensional space. For it combiningthe advantages of TRCR model and9+-intersection model and at the same time introducing thethought of dimension widening of3D9-intersection model, its ability to expressing is morepowerful. After improvement and optimization, this model will have more applications insolving practical problems.