Spatial Relationship Expression And Computation Model Based On Geometric Algebra

Geographic spatial relationships plays an important role in the process of spatial data modeling, spatial query and analysis, spatial formal expression and reasoning. At present, spatial relations research mainly focus on the qualitative description method, formal expression and space-time reasoning, and also the quantitative calculation. But in GIS it involves the space target position and attributes, how to use the geometry and topology information is the key of spatial relation analysis.Firstly, we discuss the unified expression of multidimensional objects. Based on the blade expression of geometry primitives and the multivector expression of complex space object, we realize hierarchy structure to express the multi-dimensional space object, and through multivector coding, we embed the semantic and attributes information in the expression of structure.Then we discuss the spatial relationship expression between multi-dimensional objects. Based on the expression structure, storage structure and properties characteristics of space object in geometric algebra, we build the spatial relation description and expression between simple objects, such as topology, orientation, measurement, and on this basis we explore the spatial relationships formalization between complex objects. Details are:①The topology relation, by adopting the method of half qualitative representation and reasoning, constructing the decision tree to formal modeling between multi-dimensional objects, which important thing is selecting the corresponding relation judgment operators for key nodes, and adding the corresponding constraint rules.②The position relation, by adopting the method of quantitative expression, computing the angles between simple objects, such as the points, lines, regions. Then using calculus method to discuss the orientation relations between complex objects.③The metric relations, also use quantitative methods, expressing the maximum, minimum distance between the simple objects, then we deduce the relationship between complex objects using derived method.And then we discuss the spatial relation calculation between multi-dimensional object. In view of the existing GIS spatial calculation algorithm is difficult to satisfy the unity expression and computing of different types, different dimensions, we try to construct a calculation process on the demand of different spatial analysis. Key steps are:①Analysis the solving process of typical space calculation problem under the framework of geometric algebra instead of the Euclidean space;②Uing geometric algebra operators library to decomposition the key steps, forming composite operators;③Using geometric algebra operators and algorithms to control and regulate the attributes, semantic state during the computing, which is efficient to calculate spatial relations.Finally, in case verification section, the paper focuses on analyzing the intersection between the multi-dimensional object. For example, triangulation intersection algorithm, we design the building process under the framework of geometric algebra, and compare the efficiency and the analysis results with traditional methods, then we get the answer, the logic structure of the algorithm based on geometric algebra is simple, and also efficiency. It provides the reference for other complex object modeling and spatial analysis.