基于几何代数的空间关系表达与计算模型研究
发布时间：2019-03-20 15:42
【摘要】：GIS中地理对象间的空间关系分析在空间数据建模、空间查询与分析,形式化表达与推理等过程中起着重要作用。目前空间关系研究,有偏定性的空间关系描述方法、形式化表达和时空推理,也有偏定量的空间关系计算。如何结合空间目标的位置和属性特征,利用这些几何与拓扑信息,是空间关系分析的关键。 在多维对象的统一表达方面,论文依托Clifford代数,基于blade的几何基元表达和多重向量的复杂对象表达,实现多维空间对象的层次结构表达,并通过多重向量编码结构,将地理对象的空间语义与属性信息嵌入到其表达结构中。 在多维对象间空间关系表达方面,论文基于几何代数空间对象的表达结构、存储结构和属性特征,构建简单空间对象间的拓扑、方位和度量关系的描述与表达,并在此基础上探讨复杂对象间空间关系的形式化表达。其中：①拓扑关系,采用半定性方法表示和推理,通过构建决策树方法对多维对象进行拓扑关系的形式化建模,重点是在关键节点处选择相应的关系判断算子,并添加相应的约束规则；②方位关系,采用定量方法,利用点、线段、区域之间的角度信息来推导简单对象的方位关系,继而采用演算方法推导复杂对象间方位关系的形式化表达；③度量关系,采用定量方法表达,利用简单对象间的最大、最小距离信息,同样采用演算方法推导了复杂对象间度量关系的形式化表达。 在多维对象间空间关系计算方面,论文针对现有GIS空间计算算法难以满足不同类型、不同维度对象的统一表达与计算问题,尝试构建面向不同空间分析需求的计算流程。关键步骤为：①分析欧氏空间中典型空间计算问题在几何代数框架下的求解流程；②利用几何代数中丰富的算子算法库,对分解出来的空间计算流程中的关键步骤加以分析求解,形成空间计算求解的复合算子；③利用几何代数算子算法集中的空间约束求解子集对空间计算过程中空间数据的属性、语义状态加以控制和调控,便于高效快速地进行空间关系计算。 最后,案例验证部分,论文着重分析了多维对象间求交关系,以三角网求交算法为例,设计其在几何代数框架下构建流程,并与传统算法进行了效率对比与结果分析,结果表明基于几何代数的算法流程逻辑结构简单、运算高效,这为其它复杂对象间建模表达与空间分析统一求解提供了借鉴。
[Abstract]:The spatial relationship analysis between geographical objects in GIS plays an important role in spatial data modeling, spatial query and analysis, formal expression and reasoning. At present, the spatial relationship research, the meta-qualitative spatial relationship description method, the formal expression and the space-time reasoning, also have a partial quantitative spatial relationship calculation. How to combine the location and attribute of the space object is the key to the spatial relationship analysis using these geometric and topological information. In the aspect of the uniform expression of the multi-dimensional object, the paper relies on the Clifford algebra, and based on the geometric primitive expression of the blade and the complex object expression of the multiple vectors, the hierarchical representation of the multi-dimensional space object is realized, and the multi-dimensional object is coded by the multiple vectors. structure for embedding spatial semantic and attribute information of a geographical object into its expression structure In that aspect of the expression of the space relation between the multi-dimensional object, the paper construct a description of the relation between the topology, the orientation and the measure of the simple space object based on the expression structure, the storage structure and the attribute characteristic of the space object of the geometric algebra. In this paper, the form of spatial relationship between complex objects is discussed. The method comprises the following steps of: carrying out formal modeling of the topological relation of a multi-dimensional object by constructing a decision tree method by using a semi-qualitative method representation and a reasoning, and mainly selecting a corresponding relation judgment operator at the key node, and adding a corresponding constraint rule; and the invention A quantitative method is used to derive the orientation relation of a simple object by using the angle information between a point, a line segment and a region, The maximum and minimum distance information of complex objects is also derived by the calculation method. In the aspect of multi-dimensional object space relation calculation, the paper aims at the problem that the existing GIS space calculation algorithm is difficult to meet the unified expression and calculation of different types and different dimension objects, and tries to construct the demand for different space analysis The key steps are as follows: the solution flow of the typical space calculation problem in the Euclidean space under the geometric algebra frame is analyzed, and the key steps in the decomposed space calculation process are added by using the rich operator algorithm library in the geometric algebra. By means of analysis and solution, a complex operator for spatial calculation is formed, and the spatial constraint solution set in the geometric algebraic operator algorithm is used to solve the attribute of spatial data in the space calculation process, the semantic state is controlled and controlled, In the end, the case verification part and the thesis focus on the analysis of the relationship between the multi-dimensional objects. Taking the triangular mesh intersection algorithm as an example, it is designed to construct the flow under the framework of the geometric algebra, and the efficiency is compared with the traditional algorithm. The comparison and result analysis show that the algorithm flow logic structure based on the geometric algebra is simple, and the operation is high and efficient, which is the unity of the modeling expression and the space analysis among other complex objects.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208
本文编号：2444356
[Abstract]:The spatial relationship analysis between geographical objects in GIS plays an important role in spatial data modeling, spatial query and analysis, formal expression and reasoning. At present, the spatial relationship research, the meta-qualitative spatial relationship description method, the formal expression and the space-time reasoning, also have a partial quantitative spatial relationship calculation. How to combine the location and attribute of the space object is the key to the spatial relationship analysis using these geometric and topological information. In the aspect of the uniform expression of the multi-dimensional object, the paper relies on the Clifford algebra, and based on the geometric primitive expression of the blade and the complex object expression of the multiple vectors, the hierarchical representation of the multi-dimensional space object is realized, and the multi-dimensional object is coded by the multiple vectors. structure for embedding spatial semantic and attribute information of a geographical object into its expression structure In that aspect of the expression of the space relation between the multi-dimensional object, the paper construct a description of the relation between the topology, the orientation and the measure of the simple space object based on the expression structure, the storage structure and the attribute characteristic of the space object of the geometric algebra. In this paper, the form of spatial relationship between complex objects is discussed. The method comprises the following steps of: carrying out formal modeling of the topological relation of a multi-dimensional object by constructing a decision tree method by using a semi-qualitative method representation and a reasoning, and mainly selecting a corresponding relation judgment operator at the key node, and adding a corresponding constraint rule; and the invention A quantitative method is used to derive the orientation relation of a simple object by using the angle information between a point, a line segment and a region, The maximum and minimum distance information of complex objects is also derived by the calculation method. In the aspect of multi-dimensional object space relation calculation, the paper aims at the problem that the existing GIS space calculation algorithm is difficult to meet the unified expression and calculation of different types and different dimension objects, and tries to construct the demand for different space analysis The key steps are as follows: the solution flow of the typical space calculation problem in the Euclidean space under the geometric algebra frame is analyzed, and the key steps in the decomposed space calculation process are added by using the rich operator algorithm library in the geometric algebra. By means of analysis and solution, a complex operator for spatial calculation is formed, and the spatial constraint solution set in the geometric algebraic operator algorithm is used to solve the attribute of spatial data in the space calculation process, the semantic state is controlled and controlled, In the end, the case verification part and the thesis focus on the analysis of the relationship between the multi-dimensional objects. Taking the triangular mesh intersection algorithm as an example, it is designed to construct the flow under the framework of the geometric algebra, and the efficiency is compared with the traditional algorithm. The comparison and result analysis show that the algorithm flow logic structure based on the geometric algebra is simple, and the operation is high and efficient, which is the unity of the modeling expression and the space analysis among other complex objects.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P208
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