基于几何代数的三维地籍空间数据模型研究

发布时间：2018-04-24 22:35

本文选题：三维地籍 + 空间数据模型　；参考：《中国矿业大学》2016年博士论文

【摘要】：随着社会经济的快速发展,城市地区人口数量的激增和土地资源有限性之间的矛盾日益突出。为了更加高效率的利用有限的土地资源,城市土地利用方式逐步向立体化、复杂化方向发展。这种立体化的土地利用方式给传统二维地籍管理带来了巨大的挑战,以二维宗地为地籍管理和登记单元的传统地籍无法对城市复杂的土地利用方式及其三维空间中土地权利归属进行清晰、准确的表达。三维地籍作为未来地籍管理发展的主要方向,通过对城市区域内的三维权利空间进行立体化的分割和表达,可以对当前城市区域复杂的土地利用方式进行有效管理。三维地籍空间数据模型的研究和构建是实现三维地籍管理的基础,它涉及三维地籍权利空间的划分方式、三维地籍对象的数据组织和表达形式、地籍宗地的可视化及空间关系分析计算等多个方面内容。三维地籍空间数据模型的研究和构建以现有三维空间数据模型为基础,是后者在地籍管理领域的应用。综合现有三维空间数据模型的特征和地籍管理对空间数据对象表达的特殊要求,当前三维地籍空间数据模型的构建大多以边界表达模型为基础,侧重于地籍权属边界和拓扑构造关系的描述。基于欧氏几何构建的边界表达模型通过不同维度对象相互之间的拓扑构造关系间接表达相应几何信息,实质上属于拓扑关系表达模型,缺乏对边界几何信息的直接描述;同时,欧氏空间中几何运算依赖于特定的坐标系统,不同维度之间的计算框架差异巨大。欧氏几何的上述局限性导致基于边界表达模型构建的三维地籍空间数据模型难以实现三维地籍空间中空间拓扑关系的分析和计算。为了解决基于欧氏几何构建的三维地籍空间数据模型遇到的问题,本文借鉴几何代数理论在多维GIS研究中的应用,尝试将几何代数引入到三维地籍空间数据建模领域,从数学实现的底层框架进行创新,弥补基于欧氏几何构建的三维地籍数据模型在三维空间分析中的不足。本文利用几何代数在拓扑关系与几何信息统一表达、几何运算的代数化及其坐标无关性和维度无关性等方面的优势,构建了基于几何代数的三维地籍空间数据模型。本文的主要研究内容和取得的主要研究成果包括以下几个方面:(1)本文对当前国内外学者在三维地籍管理领域的相关研究成果进行了分析和讨论,研究了地籍管理领域和几何代数中相关的基本概念,提出了三维地籍登记单元的定义和三维权属空间的划分方式,阐述了几何代数中的基本运算、常见的几何代数系统及共形几何代数空间中的基本几何对象的表达。论文对当前三维空间数据模型进行了分类和总结,讨论了模型的优点和不足及其地籍建模领域的适应性。(2)基于当前三维空间数据模型发展现状和几何代数在GIS研究领域的应用,本文提出了基于几何代数的三维地籍空间数据模型。文章对三维地籍建模对象进行了抽象和维度划分,在此基础上,研究了共形空间中地籍对象的几何与拓扑关系表达。利用几何代数在维度扩展方面的优势,实现了不同维度地籍对象表达形式的统一。在共形空间中,以多重向量结构进行组织和表达地籍宗地,宗地的几何与拓扑关系统一于多重向量结构中,实现了地籍宗地几何信息与拓扑关系表达的统一。(3)对三维地籍空间中的拓扑关系表达和计算进行了研究。在对当前空间拓扑关系研究现状及其在地籍领域的应用分析总结的基础上,研究了三维地籍对象的内部拓扑构造关系和对象之间的外部拓扑关系。用于表达三维地籍对象的多重向量结构中清晰的包含了对象内部的拓扑构造关系,在对地籍对象几何信息进行外积构造表达的同时,实现了不同维度地籍对象拓扑构造关系的描述。在研究三维地籍空间对象外部空间拓扑关系过程中,依据三维地籍空间数据特征,对三维地籍对象之间的外部拓扑关系进行了分类研究,给出了75种外部拓扑关系,并利用几何代数基本算子,对共形空间中基本几何对象之间的拓扑关系计算规则进行了分类研究,推导了共形空间中点、线、面之间相离、相交、包含等拓扑关系判断规则。在此基础上,结合地籍对象的共形表达给出了基于几何代数的三维地籍空间对象之间外部拓扑关系分析计算框架。文章按照计算方式的不同将三维地籍空间对象之间的外部拓扑关系进行了分类研究,提出了每种类型拓扑关系的分析和计算方法。(4)在三维地籍空间拓扑关系分析计算的基础上,研究了三维地籍空间中的基于几何代数表达的宗地更新算法,提出了基于多重向量结构的地籍宗地自适应更新算法,并以三维宗地体的合并和分割为例对算法的实现进行了实例推演。(5)构建了基于几何代数的三维地籍原型系统,对本文提出的基于几何代数的三维地籍空间数据模型及其关键技术进行了系统实现和案例分析,进一步验证了本文研究内容和相关成果的有效性和可行性。
[Abstract]:With the rapid development of the social economy, the contradiction between the population growth of urban areas and the limited land resources is becoming increasingly prominent. In order to make more efficient use of limited land resources, the way of urban land use is gradually stereoscopic and complicated. The three-dimensional land use mode is given to the traditional two dimensional cadastral management. The traditional cadastre of two dimensional land as cadastral management and registration unit can not make a clear and accurate expression of the complex land use and the ownership of land in the three-dimensional space. The three-dimensional cadastre is the main direction of the development of the future cadastral management, through the three-dimensional right space in the urban area. Three-dimensional cadastral spatial data model is the basis of three-dimensional cadastral management, which involves the division of three-dimensional cadastral rights space, the data organization and expression of three-dimensional cadastral objects, cadastral sect. The research and construction of 3D Cadastre spatial data model is based on the existing 3D spatial data model and the application of the latter in the cadastral management field. The current three-dimensional cadastral spatial data model is mostly based on the boundary expression model, focusing on the description of the cadastral authority boundary and the topological structure relationship. The boundary expression model based on the Euclidean geometry constructs the corresponding geometric information indirectly through the topological structure relationship between different dimensional objects, which is essentially a topological relation. At the same time, the geometric operations in Euclidean space are dependent on a specific coordinate system, and the computational frameworks of different dimensions are very different. The above limitations of Euclidean geometry lead to a three-dimensional cadastral spatial data model based on the boundary expression model which is difficult to realize three-dimensional cadastral space. In order to solve the problems encountered in the three-dimensional cadastral spatial data model based on Euclidean geometry, this paper attempts to introduce geometric algebra into the 3D cadastral spatial data modeling domain by using geometric algebra to solve the problems encountered in the three-dimensional cadastral spatial data model based on Euclidean geometry. In this paper, a three-dimensional cadastral spatial data model based on geometric algebra is constructed by using geometric algebra to express the topological relations and geometric information uniformly, the algebraic transformation of geometric operations and the independence of coordinates and dimensionality. The main research contents and main achievements of this paper include the following aspects: (1) this paper analyzes and discusses the relevant research achievements of scholars at home and abroad in the field of three-dimensional cadastral management, studies the basic concepts related to cadastral management and geometric algebra, and puts forward the definition of three-dimensional cadastral registration unit. This paper expounds the basic operations in geometric algebra, the common geometric algebra system and the expression of the basic geometric objects in the conformal geometric algebra space. This paper classifies and summarizes the current three-dimensional spatial data model, and discusses the advantages and disadvantages of the model and the adaptability of the cadastral modeling field. (2) based on the current development of three-dimensional spatial data model and the application of geometric algebra in the field of GIS research, this paper presents a three-dimensional cadastral spatial data model based on geometric algebra. This paper makes abstract and dimensional division of 3D Cadastre modeling objects. On this basis, the geometry and topology of cadastral objects in conformal space are studied. With the advantage of geometric algebra in dimension expansion, the expression of cadastral objects in different dimensions is unified. In conformal space, the cadastral land is organized and expressed with multiple vector structures. The geometric and topological relations of the clan are unified in multiple vector structures, and the geometric and topological relations of cadastral sites are realized. (3) the expression and calculation of topological relations in three-dimensional cadastral space are studied. On the basis of current research status of spatial topology and its application in cadastre field, the internal topological structure relationship and external topological relations between objects are studied. The multiple vector structure of the cadastral object clearly contains the topological structure relationship within the object, and the representation of the geometric information of the cadastral objects, and the description of the topological structure relation of the different dimensions of cadastral objects. This paper classifies the external topological relations between 3D Cadastre objects, gives 75 kinds of external topological relations, and uses geometric algebra basic operators to classify the topological relation calculation rules between basic geometric objects in conformal space, and deduces the separation and intersection of points, lines and surfaces in conformal space. On this basis, based on the conformal expression of cadastral objects, an analysis and calculation framework of external topological relations between objects of three-dimensional cadastre spatial objects based on geometric algebra is given. The article classifies the outer topology of the three-dimensional cadastre space objects according to the different calculation methods. The analysis and calculation method of each type of topological relation. (4) based on the analysis and calculation of the three-dimensional cadastral spatial topological relations, this paper studies the reconstruction algorithm of the three dimensional cadastral space based on geometric algebra expression, and proposes an adaptive updating algorithm of cadastral land based on multiple vector structures, and combines and divides the three dimensional land. For example, an example is given for the implementation of the algorithm. (5) a three-dimensional cadastre prototype system based on geometric algebra is constructed. The three-dimensional cadastral spatial data model based on geometric algebra and its key technologies are systematically implemented and analyzed. The validity and feasibility of the research content and related results are further verified. Sex.

【学位授予单位】：中国矿业大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P273

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