The Research On Cardinal Direction Relations Based On MBR

With the development and application of the spatial database technology and geographic information systems (GIS), the basic theories of spatial reasoning and the arithmetic corresponding to them are innovating and developing. At present, spatial reasoning mainly consists of topological relation reasoning, cardinal direction relation reasoning and distance relation reasoning, and so on. As an important division of the spatial reasoning, the cardinal direction relation reasoning has received more and more attentions.The direction relation model is crucially important in the research for the spatial cardinal direction relation reasoning. This paper does some researches and comparisons on the existing direction relation models and uses the nine-direction relation model that is suitable for the operation on spatial relations. The spatial data types which are usually used in the research for the spatial direction relation contains"points","lines"and"polygons"."Polygon"object is usually realized in form of the Minimum Bounding Rectangle (MBR) in the spatial database. This paper takes advantage of interval algebra and rectangle algebra theories. and brings forward a new reasoning method based on combination of the MBR model's cardinal direction relation and rectangle algebra relation; And provides the composing method based on the direction relation matrix by using the direction relation matrix to denote the direction relations between the objects'MBRs.This paper firstly discusses the spatial cardinal direction reasoning based on the point object, and then develops it into the cardinal direction relation reasoning problem based on the object's MBR. Combining the famous Balbiani's rectangle algebra theory, this paper provides a new model based on the combination of the cardinal direction object's MBR and the rectangle relation algebra. Using the model, the nicer computing character of the rectangle algebra can be well applied in the spatial direction reasoning, which greatly reduced the difficulty of direction relations reasoning, and the consistency verification of the cardinal direction relation based on the rectangle algebra is implemented.As for the direction relations composing problems based on the MBR, this paper uses direction relation matrix to denote the direction relation among the objects'MBRs. According to a series of the definitions put forward on the direction relation matrix's character and computation, the theorem has provided the method to answer the problem on the composing between direction relations based on the matrix. Aim at the problem about the inconsistent of some composing results from the direction relation model based on the MBR ,this paper construct two information models :depth direction relations matrix and 5×5 direction relations matrix and put forward the method to answer the composing problem using 5×5 direction relation matrix.