本文關(guān)鍵詞： 共形幾何代數(shù) 時(shí)空拓?fù)潢P(guān)系 形式化表達(dá) 計(jì)算框架 決策樹　出處：《浙江大學(xué)》2014年博士論文　論文類型：學(xué)位論文

【摘要】：時(shí)空拓?fù)浞治鍪堑乩硇畔⒖茖W(xué)的重要研究課題。目前,研究者們對(duì)時(shí)空拓?fù)潢P(guān)系普遍采用定性的方法進(jìn)行表達(dá)。這些方法或多或少存在著內(nèi)容重復(fù)、信息冗余等問題,且不具備直接計(jì)算時(shí)空拓?fù)潢P(guān)系的能力。而國(guó)內(nèi)外有關(guān)時(shí)空拓?fù)潢P(guān)系計(jì)算的研究也比較有限,尚未有一套較為系統(tǒng)的理論、方法體系。受底層數(shù)學(xué)理論基礎(chǔ)的制約,時(shí)空對(duì)象的表達(dá)與時(shí)空拓?fù)潢P(guān)系的表達(dá)彼此分離,較難定義相對(duì)完備的時(shí)空拓?fù)浞治鏊阕訉?duì)時(shí)空拓?fù)潢P(guān)系進(jìn)行統(tǒng)一表達(dá)與計(jì)算。 本文針對(duì)現(xiàn)有時(shí)空拓?fù)潢P(guān)系表達(dá)與計(jì)算方法存在的不足,圍繞時(shí)空對(duì)象表達(dá)與時(shí)空拓?fù)浞治鰬?yīng)用需求,從多維時(shí)空統(tǒng)一視角出發(fā),引入具有多維統(tǒng)一表達(dá)與幾何計(jì)算能力的共形幾何代數(shù)理論,為不同類型、不同維度的時(shí)空對(duì)象建立有機(jī)統(tǒng)一的表達(dá)模型,并在此基礎(chǔ)上提出時(shí)空拓?fù)湫问交磉_(dá)方法與統(tǒng)一計(jì)算框架,為地理對(duì)象間的時(shí)空拓?fù)潢P(guān)系表達(dá)與計(jì)算提供了理論依據(jù)和方法支撐,有效提升了GIS的時(shí)空拓?fù)潢P(guān)系表達(dá)與分析能力。本文的研究?jī)?nèi)容具體如下： (1)基于共形幾何代數(shù)的多維時(shí)空對(duì)象統(tǒng)一表達(dá)模型。針對(duì)目前不同類型、不同維度時(shí)空對(duì)象表達(dá)模式不統(tǒng)一的問題,引入共形幾何代數(shù)理論,將不同維度的復(fù)雜時(shí)空對(duì)象分解為若干簡(jiǎn)單幾何形體,利用外積和內(nèi)積進(jìn)行時(shí)空構(gòu)建與時(shí)空對(duì)象表達(dá),構(gòu)造基于多重向量的時(shí)空對(duì)象統(tǒng)一表達(dá)模型。 (2)共形幾何代數(shù)支持下的時(shí)空拓?fù)潢P(guān)系形式化表達(dá)。基于上述構(gòu)建的多維時(shí)空對(duì)象統(tǒng)一表達(dá)模型,使用定量與定性相結(jié)合的多分支決策樹方法對(duì)時(shí)空拓?fù)潢P(guān)系進(jìn)行形式化表達(dá),利用拓?fù)潢P(guān)系判斷規(guī)則集推導(dǎo)簡(jiǎn)單時(shí)空對(duì)象之間的拓?fù)潢P(guān)系,并進(jìn)一步對(duì)復(fù)雜對(duì)象之間的時(shí)空拓?fù)潢P(guān)系進(jìn)行推演,實(shí)現(xiàn)時(shí)空對(duì)象表達(dá)與時(shí)空拓?fù)潢P(guān)系表達(dá)的有機(jī)統(tǒng)一。 (3)共形幾何代數(shù)支持下的時(shí)空拓?fù)潢P(guān)系統(tǒng)一計(jì)算框架。在時(shí)空拓?fù)潢P(guān)系形式化表達(dá)的基礎(chǔ)上,研究歐氏空間中常用拓?fù)潢P(guān)系計(jì)算方法在共形幾何代數(shù)框架下的算法結(jié)構(gòu)與實(shí)現(xiàn)流程,構(gòu)建實(shí)用的時(shí)空拓?fù)潢P(guān)系算子、算法集,設(shè)計(jì)時(shí)空統(tǒng)一的拓?fù)潢P(guān)系計(jì)算框架STTR-CF,實(shí)現(xiàn)時(shí)空拓?fù)潢P(guān)系計(jì)算引擎與運(yùn)算接口。 (4)應(yīng)用示范與實(shí)例驗(yàn)證。利用STTR-CF提供的時(shí)空拓?fù)潢P(guān)系運(yùn)算接口進(jìn)行土地利用現(xiàn)狀數(shù)據(jù)拓?fù)錂z查、歷史回溯等應(yīng)用示范,并與其它方法所得結(jié)果進(jìn)行比較以驗(yàn)證STTR-CF的可行性、有效性及其計(jì)算結(jié)果的正確性。 研究表明,基于共形幾何代數(shù)的時(shí)空對(duì)象統(tǒng)一表達(dá)模型具有多維統(tǒng)一、結(jié)構(gòu)自適應(yīng)、幾何意義明確等特性,能夠有效支撐時(shí)空拓?fù)潢P(guān)系的統(tǒng)一表達(dá)與計(jì)算。本文設(shè)計(jì)并實(shí)現(xiàn)的時(shí)空拓?fù)潢P(guān)系統(tǒng)一計(jì)算框架STTR-CF,可針對(duì)具體的需求和問題構(gòu)建合適的解決方案,有效促進(jìn)了時(shí)空一體化分析與應(yīng)用。本文的研究工作為時(shí)空拓?fù)潢P(guān)系的表達(dá)與計(jì)算提供了一條可行的新途徑,具有重要的科學(xué)意義與實(shí)用價(jià)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.

【學(xué)位授予單位】：浙江大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2014
【分類號(hào)】：P208

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