共形几何代数支持下的时空拓扑关系表达与计算研究

发布时间：2018-02-26 06:00

本文关键词： 共形几何代数时空拓扑关系形式化表达计算框架决策树　出处：《浙江大学》2014年博士论文　论文类型：学位论文

【摘要】：时空拓扑分析是地理信息科学的重要研究课题。目前,研究者们对时空拓扑关系普遍采用定性的方法进行表达。这些方法或多或少存在着内容重复、信息冗余等问题,且不具备直接计算时空拓扑关系的能力。而国内外有关时空拓扑关系计算的研究也比较有限,尚未有一套较为系统的理论、方法体系。受底层数学理论基础的制约,时空对象的表达与时空拓扑关系的表达彼此分离,较难定义相对完备的时空拓扑分析算子对时空拓扑关系进行统一表达与计算。本文针对现有时空拓扑关系表达与计算方法存在的不足,围绕时空对象表达与时空拓扑分析应用需求,从多维时空统一视角出发,引入具有多维统一表达与几何计算能力的共形几何代数理论,为不同类型、不同维度的时空对象建立有机统一的表达模型,并在此基础上提出时空拓扑形式化表达方法与统一计算框架,为地理对象间的时空拓扑关系表达与计算提供了理论依据和方法支撑,有效提升了GIS的时空拓扑关系表达与分析能力。本文的研究内容具体如下： (1)基于共形几何代数的多维时空对象统一表达模型。针对目前不同类型、不同维度时空对象表达模式不统一的问题,引入共形几何代数理论,将不同维度的复杂时空对象分解为若干简单几何形体,利用外积和内积进行时空构建与时空对象表达,构造基于多重向量的时空对象统一表达模型。 (2)共形几何代数支持下的时空拓扑关系形式化表达。基于上述构建的多维时空对象统一表达模型,使用定量与定性相结合的多分支决策树方法对时空拓扑关系进行形式化表达,利用拓扑关系判断规则集推导简单时空对象之间的拓扑关系,并进一步对复杂对象之间的时空拓扑关系进行推演,实现时空对象表达与时空拓扑关系表达的有机统一。 (3)共形几何代数支持下的时空拓扑关系统一计算框架。在时空拓扑关系形式化表达的基础上,研究欧氏空间中常用拓扑关系计算方法在共形几何代数框架下的算法结构与实现流程,构建实用的时空拓扑关系算子、算法集,设计时空统一的拓扑关系计算框架STTR-CF,实现时空拓扑关系计算引擎与运算接口。 (4)应用示范与实例验证。利用STTR-CF提供的时空拓扑关系运算接口进行土地利用现状数据拓扑检查、历史回溯等应用示范,并与其它方法所得结果进行比较以验证STTR-CF的可行性、有效性及其计算结果的正确性。研究表明,基于共形几何代数的时空对象统一表达模型具有多维统一、结构自适应、几何意义明确等特性,能够有效支撑时空拓扑关系的统一表达与计算。本文设计并实现的时空拓扑关系统一计算框架STTR-CF,可针对具体的需求和问题构建合适的解决方案,有效促进了时空一体化分析与应用。本文的研究工作为时空拓扑关系的表达与计算提供了一条可行的新途径,具有重要的科学意义与实用价值。
[Abstract]:Spatio temporal topology analysis is an important research topic in geographic information science. At present, the researchers on the spatio-temporal topological relationship generally adopts the qualitative method of expression. These methods are more or less repetitive, information redundancy, and do not have the ability to directly calculate the relationship of spatio-temporal topology at home and abroad. The research and calculation of spatio-temporal topological relation is relatively limited, there is not a set of systematic theory and method system. Restricted by the underlying mathematical theory, separated from each other and the expression of spatio-temporal topological relationship of spatio-temporal objects, is difficult to define the spatio-temporal topological complete analysis of spatio-temporal topological relationship operator unified expression and calculation.
Problems and calculation methods of the existing spatio-temporal topological relationship expression, around the spatio-temporal object expression and spatio-temporal topology analysis of application requirements, starting from the perspective of multi-dimensional unified, unified expression is introduced into the multi-dimensional conformal geometric algebra and geometry calculation ability, different types of expression model of the organic unity of the spatio-temporal objects of different dimensions, based on the space-time topology formal expression method and unified computing framework, provides the theory basis and method support and calculation for geographic spatio-temporal topological relations of objects, effectively enhance the expression of spatio-temporal topological relationship and analysis of GIS. The research contents of this paper are as follows:
(1) the expression of the unified model of multidimensional space object based on conformal geometric algebra. Aiming at the different types of models, unified problems of different dimensions of spatio-temporal expression, the conformal geometric algebra theory, the complex spatio-temporal objects of different dimensions are decomposed into several simple geometric shape, the outer product and inner product of space-time expression and construction spatiotemporal object, time-space multiple vector based unified object representation model.
(2) the conformal geometric algebra topological relations model support expression. Expression of the uniform model based on the multidimensional space object, multi branch decision tree method using a combination of qualitative and quantitative analysis on the relationship between the spatio-temporal topological representation of topological relations between the topological relation judgment rule set is simple spatio-temporal objects and, further deduction of spatio-temporal topological relationship between complex objects, to achieve the organic unity of the relationship between the expression of spatial object expression and spatio-temporal topology.
(3) the conformal geometric algebra unified spatio-temporal topological relationship under the support of the computing framework. Based on the expression of topological relations model on the common topology of Euclidean space relation calculation method in conformal geometric algebra algorithm structure framework and implementation process, construct spatio-temporal topological relationship operator, practical algorithms, computing framework the STTR-CF topology design of space-time unified computing engine and operation interface, spatio-temporal topological relationship.
(4) application demonstration and example verification. The spatio-temporal topological relation computing interface provided by STTR-CF land use data topology check, historical review and application demonstration, and the results were compared with other methods to validate the validity of STTR-CF, and the calculation results.
Research shows that the unified spatio-temporal conformal geometric algebra expression model with multidimensional unity based on adaptive structure, clear geometric meaning and other characteristics, can effectively support the unified spatio-temporal topological relationship between expression and calculation. Spatio-temporal topological relation of unity of the design and implementation of computing framework STTR-CF, according to the specific needs and problems of building the right solution the effective promotion of the integration of spatial analysis and application. The research work provides a new feasible way for the expression and calculation of topological relations, has important scientific significance and practical value.

【学位授予单位】：浙江大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：P208

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