Formal Expression And Parallel Computing Method Of Spatial Relationship Based On Conformal Geometric Algebra

In geographic information system,the expression and calculation of spatial relations between geographic objects is one of the focuses of scholars’ research.The analysis,expression and calculation of spatial relations are the important foundation of spatial data modeling.In this paper,based on conformal geometry algebra,the concept of blades product is used to realize the formal expression of basic geographic objects based on multiple vectors,and then the spatial relations are calculated according to the operator library of conformal geometry algebra and custom operators.For multi-dimensional space objects,the features and attributes of geographic entity objects are embedded into the formal expression with the help of multi-vector coding structure,and the computational efficiency is improved with the help of pre-multiplication table by the use of vector coding,and each component of the multi-vector is operated in parallel.In the present study of spatial relations,mathematical tools are combined to realize the integrated expression of spatial objects and spatial relations.For the formal expression of multidimensional objects,it is extended to the description and expression of simple spatial objects such as topological relation,metric relation and position relation based on the construction of basic elements,and then the expression is extended to complex spatial objects and spatial relations.In the topological relation,the formal expression of the definition of intersection operator and decision tree is used to judge and describe the topological relation between multidimensional objects.The emphasis is on the self-defined judgment operator,which determines the node elements of the decision tree.In the metric relation,the quantitative description method is directly adopted,and It’s represented by the magnitude of the Angle.Firstly,the position relation between point and line,line and line,point and region is inferred.Finally,the derivation of the position relation between complex objects is obtained.In the metric relation,quantitative method is used to describe it.The minimum distance and maximum distance between simple objects are directly used to measure it,which is a range value.Finally,the metric relation of complex objects is obtained through calculation and derivation.This paper adds constraint rules to the spatial relationships of basic spatial objects,designs a calculation model for spatial relationships among complex objects,and builds a framework for analyzing and solving spatial relationships between objects of different types and dimensions.In this model,the basic vector in the conformal geometric algebra is described by binary bits in the computer.According to the hierarchical relationship of the multiple vectors in the conformal geometric algebra,the parallel calculation method is adopted to improve the efficiency.As the example of triangulation network intersecting algorithm,according to the comparison of the intersecting result with the traditional vector method and scalar method,it is found that the efficiency of this model’s parallel intersecting algorithm is the highest.The research on the representation and parallel algorithm of spatial objects by using conformal geometry algebra provides a reference for the integration of representation and computation of other complex spatial objects.