An Extended Topological Relation Model Based On Intersection Component Details

The research of spatial relations includes topological relations,directional relations and metric relations.Among them,topological relations refer to the relations between spatial objects that meet the topological principles,that is,the intersection and connection of spatial objects represented by points,lines and planes.Topological relation is a qualitative description of spatial objects.Most of the present subdivision topological relation models lack in-depth analysis of spatial objects and local details.However,the specific spatial distribution details of spatial objects with the same topological elements need to be discussed differently,which means distinguishing the different intersection components between topologically equivalent space objects.In view of the uncertainty of boundary points of space objects and the diversity of intersection components of space objects,aiming at the problem that the four intersection model and nine intersection model can not effectively distinguish the complex topological relation between space objects,this paper introduces quantitative or semi-quantitative factors such as the number of intersection points and intersection lines between space objects and the contribution value of points,extend the intersection non-empty elements in the expression matrix,and construct the topological relation extension model based on the subdivision of the intersection components of spatial obj ects.The topological relations of plane-to-plane and lineto-line are subdivided,and the effectiveness and advantages of the precise expression of topological relations are verified by examples.The main research work includes:(1)This paper analyzes the elements of each intersection component when the four intersection model and nine intersection model are applied to plane-to-plane space objects,introduces the points on the boundary of plane space objects,analyzes the influence of boundary points on topological equivalence,and expresses the topological relation under the different distribution of intersection components.The four intersection and nine intersection topological relation models are extended,and their respective advantages are compared.The results of the overall node value,node distribution and intersection component subdivision are verified by experiments.(2)This paper extends the expression of line-to-line topological relation in the extended model,analyzes the difference between the result of plane-to-plane intersection and the result of line-to-line intersection,uses the ICD4I model to express the line-to-line topological relation,and verifies the feasibility and advantages of the extended model in the continuous use of lineto-line topological relation,and then discusses the solutions to the problems existing in the expression of line-to-line topological relation in the extended model.(3)This paper introduces the decomposition and combination algorithm,sets the definition of the intersection point as the decomposition point,demonstrates the decomposition results of the complex line-to-line topological relations,and explains some simple line-to-line topological relations that need to be further decomposed,obtains the meta topological relations of the lineto-line topological relations,and formulates the combination rules related to the line-to-line meta topological relations,which can be effectively expressed by the ordered arrangement of the meta topological relations The complex line-to-line topological relation is achieved.This paper explores the integrated expression of topological relation and directional relation,and solves the problems of intersection,connection and coincidence of line space objects,which will lead to the change of direction,the same topological relationship with different spatial states,and other problems.