【摘要】：GIS中地理對象間的空間關(guān)系分析在空間數(shù)據(jù)建模、空間查詢與分析,形式化表達與推理等過程中起著重要作用。目前空間關(guān)系研究,有偏定性的空間關(guān)系描述方法、形式化表達和時空推理,也有偏定量的空間關(guān)系計算。如何結(jié)合空間目標的位置和屬性特征,利用這些幾何與拓撲信息,是空間關(guān)系分析的關(guān)鍵。 在多維對象的統(tǒng)一表達方面,論文依托Clifford代數(shù),基于blade的幾何基元表達和多重向量的復(fù)雜對象表達,實現(xiàn)多維空間對象的層次結(jié)構(gòu)表達,并通過多重向量編碼結(jié)構(gòu),將地理對象的空間語義與屬性信息嵌入到其表達結(jié)構(gòu)中。 在多維對象間空間關(guān)系表達方面,論文基于幾何代數(shù)空間對象的表達結(jié)構(gòu)、存儲結(jié)構(gòu)和屬性特征,構(gòu)建簡單空間對象間的拓撲、方位和度量關(guān)系的描述與表達,并在此基礎(chǔ)上探討復(fù)雜對象間空間關(guān)系的形式化表達。其中：①拓撲關(guān)系,采用半定性方法表示和推理,通過構(gòu)建決策樹方法對多維對象進行拓撲關(guān)系的形式化建模,重點是在關(guān)鍵節(jié)點處選擇相應(yīng)的關(guān)系判斷算子,并添加相應(yīng)的約束規(guī)則；②方位關(guān)系,采用定量方法,利用點、線段、區(qū)域之間的角度信息來推導簡單對象的方位關(guān)系,繼而采用演算方法推導復(fù)雜對象間方位關(guān)系的形式化表達；③度量關(guān)系,采用定量方法表達,利用簡單對象間的最大、最小距離信息,同樣采用演算方法推導了復(fù)雜對象間度量關(guān)系的形式化表達。 在多維對象間空間關(guān)系計算方面,論文針對現(xiàn)有GIS空間計算算法難以滿足不同類型、不同維度對象的統(tǒng)一表達與計算問題,嘗試構(gòu)建面向不同空間分析需求的計算流程。關(guān)鍵步驟為：①分析歐氏空間中典型空間計算問題在幾何代數(shù)框架下的求解流程；②利用幾何代數(shù)中豐富的算子算法庫,對分解出來的空間計算流程中的關(guān)鍵步驟加以分析求解,形成空間計算求解的復(fù)合算子；③利用幾何代數(shù)算子算法集中的空間約束求解子集對空間計算過程中空間數(shù)據(jù)的屬性、語義狀態(tài)加以控制和調(diào)控,便于高效快速地進行空間關(guān)系計算。 最后,案例驗證部分,論文著重分析了多維對象間求交關(guān)系,以三角網(wǎng)求交算法為例,設(shè)計其在幾何代數(shù)框架下構(gòu)建流程,并與傳統(tǒng)算法進行了效率對比與結(jié)果分析,結(jié)果表明基于幾何代數(shù)的算法流程邏輯結(jié)構(gòu)簡單、運算高效,這為其它復(fù)雜對象間建模表達與空間分析統(tǒng)一求解提供了借鑒。
[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.
【學位授予單位】：南京師范大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：P208

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