Research On Topological Relations Between Regions With Holes

At present,the geographic information system is widely applied in many fields,while spatial analysis also becomes the research hot spot as its important symbol that distinguish from other information system.Of which the topological relations the basal study the spatial analysis,its related theory and technology have been relatively mature.The current topological relation model can well express the topological relation between simple regions or regions with holes,but it is not enough to express the details of complex interaction between regions with holes,and it does not consider the direction of regions with holes.On the basis of the existing theory,this paper studies the representation of the complex interaction details between regions with holes and the presentation and reasoning of the topological relations between directed lines and directed regions with holes.The main research contents and contributions of this thesis are concluded as follows.(1)Theoretical basis of topological relation of regions.This paper introduces point set theory and several widely used topological models,such as 4-intersection model,9-intersection model,D9-intersection model,25-intersection model,9+-intersection model and directed linedirected region model,and analyzes the advantages and disadvantages of various topological models.(2)Node-based extended 25 intersection model is proposed.Based on the 25IM,quantitative elements such as the number of intersections,node contribution value and node degree are introduced into the NE25IM to expand the non-empty intersection elements in the expression matrix,so as to achieve the purpose of fine expression of topological relationships between regions with holes.The NE25IM is used to describe the four basic topological relationships,including meet,overlap,cover and contain,between regions with holes(including the cases with one hole and two holes),and the calculation process of the intersection components of regions with holes was analyzed.Finally,an example analysis is used to verify the advantages of the NE25IM and the practical significance of the change regulation of the number of holes in regions.The results shows that the NE25IM can express the complex interaction details between the boundaries of regions with holes more directly and accurately,which intuitively reflects that the model expression numerical difference caused by the difference in the number of holes in regions with holes is related to the shape and number of holes,and expression differences of subset combinations between objects with holes vary with the types of topological relationships.(3)Directed line-directed region with one hole model is proposed.For the problem that the existing topological relation models do not consider the direction of regions with one hole and cannot accurately express the topological relations between directed lines and regions with one hole,directed line-directed region with one hole(DL-DRH)model is proposed.The DL-DRH model that considers the starting and ending points of the directed lines and the front and back faces of regions with one hole(including interior and exterior within the inner boundary).Firstly,the directed line-region with one hole(DL-RH)model is proposed,a total of 143 DL-RH topological relations between directed lines and regions with one hole are obtained and the matrix patterns and the corresponding geometric interpretations of the 143 topological relations are shown to prove the existence of the topological relations.Then,143 DL-RH topological relations are used to divide three types of DL-DRH topological relations.The computational process of converting three DL-RH topological relations into DL-DRH topological relations is analyzed,and then the DL-R model,DL-RH model and DL-DRH model presented in this research are compared.The completeness of DL-DRH topological relations is proved by using seven negative conditions.Finally,a case study(Hong Kong-Zhuhai-Macao Bridge)shows that DL-DRH model can accurately and intuitively express the topological relations between directed lines and directed regions with one hole,and the proposed seven negative conditions can be used to prove the completeness of the DL-DRH topological relations.