Research On Formal Description Model Of Spatial Direction Relationships Between Object Groups

Spatial direction relationship is one of the basic spatial relationship people must face and research when describing and expressing geo-spatial,its importance has been proved in research areas such as geo-spatial cognition,automated map generalization and so on.The description models for spatial direction relationships are important theoretical tools for computing and expressing spatial direction relationships.But the existing models are mostly used to judge spatial direction relationships between two single objects,and the researches have developed quite mature;While the researches about spatial direction relationships between object groups are only superficial and fragmentary,the only few existing models also have its own defects and deficiencies,such as cannot take types of factors which effect the spatial direction relationships between object groups into account,the computing process is too tedious,cannot realize exact quantitative calculation of spatial direction relationships between object groups and so on.In view of this,based on the theoretical methods of Delaunay triangulation,mathematical morphology and Geo-Informatics Tupu,the thesis has done systematic researches on direction relationships description models of object groups,taking factors which affect the spatial direction relationships between object groups and the defects of existing models into account.The achievements and innovations of the thesis include three aspects as follows:(1)Based on the methods of Delaunay triangulation and stripping,a solution algorithm is proposed to computing the boundary of linear/polygonal group.Its basic idea is: first,constructing constrained Delaunay triangulation of linear/polygonal group;then,getting the boundary of linear/polygonal group using the method of “stripping” with dynamic threshold,and finally building up its boundary-polygon.(2)On the basis of research(1),A qualitative description model for spatial direction relationships between object groups based on direction-relation matrix model is put forward.Its basic idea is: first,computing the MBR(minimum bounding rectangle)of reference object group,and construct its direction-relation matrix model;then,by computing the intersection of the boundary-polygon of the target object group and each direction region,finally,using the matrix to describe formally the spatial direction relationships from the reference object group to the target object group.(3)A quantitative description model for spatial direction relationships between object groups based on theories of morphological transformation and graph-spectrum is constructed.Its basic idea is: firstly,the MBR of the reference object group is computed;then a morphological transform to the reference object group is made at every specified angle interval starting from and at last stopping at the due North.After this,the spectrum density is computed by calculating the intersection of the morphological transformed reference object group and the target object group.Last,the corresponding spectrum is drawn based on analyzing the characteristics of the spectrum.The experiments were done to testing the two proposed models using geographical target pairs and map data.The experiments shows that the qualitative description model for spatial direction relationships between object groups take the effects of spatial form to spatial direction relationships into account,and it can give exact judgment to spatial direction relationships even when two object groups appears to be wind around each other and other special situations;The quantitative description model for spatial direction relationships between object groups consider the effects of spatial distance,distribution scope,distribution shape and distribution density to spatial direction relationships between object groups,besides,it can describe the spatial direction relationships between object groups intuitively and visually.The results of the two models can meet people’s habits of spatial cognition and they solve the problems of qualitative description and quantitative computations of spatial direction relationships between two object groups.