在空間資料庫中，位相空間關係可作為使用者空間資料查詢的約制條件，它提供使用者類似自然語言的語句來描述空間現象，作為與空間資料溝通的途徑。人類對空間關係的應用是一種基本的空間知識。例如：找出台灣省內所有『包含』紅樹林保護區的縣分有哪些等問題，『包含』即為一位相空間關係。目前的系統往往侷限於其特定的架構，而造成使用者與電腦溝通上的困難及訓練的增加。本論文主要目標是發展一個提供使用者以其具有的空間概念表達空間查詢需求，並可轉換為空間資料庫內部相對應空間操作之位相關係模組。
研究中藉由考量人類對位相關係的空間認知之判斷，以向量式資料為基礎，分析不同維度空間物體間交集情形之特定交集性質，歸納並定義出一組具語意概念的基本位相關係及其相應的演算法，利用該組以計算為基礎（quantitative-based）的基本位相關係，嘗試以它來描述存在於二維空間平面上的空間物體間之位相關係。最後可以使用者的空間思考為基礎，透過基本位相關係的組合來描述存在於多個物體間較為複雜的位相關係。為了提昇位相關係模組運作的效率，空間資料間的階層組織特性也被納入於位相關係模組推論機制之設計，以輔助不同階層關係間空間物體的位相關係之判斷。
本研究之目標為發展語句文字描述式之位相關係模組，研究顯示（一）經由分析向量式資料交集的情形，以四種基本的幾何演算法實行兩物體間的基本位相關係是可行的。（二）較複雜狀況的位相關係可由基本位相關係的邏輯組合加以描述與解釋。（三）明確記錄空間資料的階層關係，可增進位相關係模組運作之效率，快速地排除不必要的幾何測試。

Topological relations are often used to represent constraints for spatial queries in spatial databases. It provides us a way to communicate human with spatial data in a qualitative and natural language format we use in our daily lives. Spatial relation is a part of human’s spatial knowledge. For example , a topological relation “contain” is used in the query of “find out all countries which contain mangrove conservation area in Taiwan” to express our needs regarding spatial data. Currently commercial systems are often restricted to their specific functions , so that the communication between users and systems is difficult and training is a must. The goal of our thesis is to develop a topological relation module that allows users to present spatial queries needs with his or her spatial cognitive understanding , and later translate them into quantitative-based operations to derived request information.
In this research , by incorporating the fundamentals of humans spatial cognition , we analyze specific geometric intersections between two different-dimensional spatial objects in vector data format , and develop a set of primitive topological relations with unique semantic and geometric meanings , along with their respective algorithms. We can thus determine the topological relations between two objects in 2-D space with this quantitative-based approach. Based on the spatial thinking of humans , we can further describe more complex situations among multiple objects by combining various primitive topological relations. To improve the efficiency of the topological relation module , hierarchical organizations among spatial objects are also considered in the design of the reasoning mechanism for the module.
The goal of our research is to build a quantitative-based topological relation module that allows users to interact with GIS systems with already familiar qualitative , natural language-like topological relations. The result of our research shows that , firstly , the conceptual design and the implementation of the primitive topological relation module in computers is possible , secondly , more complex topological situations can be described and explained with logical combination of the proposed primitive topological relations , finally , explicitly stored hierarchical organization of spatial data can improve the efficiency of the module during query processing by quickly excluding unnecessary test.

中文摘要……………………………………………………………….Ⅰ
英文摘要……………………………………………………………….Ⅱ
致謝…………………………………………………………………….Ⅳ
目錄………………………………………………………………….…Ⅴ
表目錄……………………………………………………………….….Ⅶ
圖目錄…………………………………………………………………..Ⅸ
第一章 緒論……………………………………………………………1
§1-1 研究背景與動機………………………………………………...1
§1-2 研究方法與流程……………………………………………...…2
§1-3 論文組織………………………………………………………...6
第二章 位相關係的相關理論探討……………………………………7
§2-1 位相關係的模式化及其應用…………………………………...8
§2-2 位相關係模式化的理論回顧……………………………….…11
§2-2-1 Point-Set理論………………………………………….11
§2-2-2 Order理論……………………………………………...19
§2-2-3 Formal Logic理論……………………………………..21
§2-2-4 Image-Schemata理論………………………………….22
§2-2-5 運用空間資料庫技術的方法………………………...23
§2-3 位相關係模式化的考量準則………………………………….25
第三章 基本位相關係模組之建立…………………………………..27
§3-1 基本位相關係的定義……………………………………….…27
§3-1-1 點、線段、面空間資料型態的定義…………………..27
§3-1-2 以交集觀點分析基本位相關係……………………...28
§3-1-3 基本位相關係的交集性質之討論………………...…37
§3-2基本位相關係的分析…………………………………………..41
§3-2-1 基本位相關係的性質………………………………...41
§3-2-2 基本位相關係與位相關係模組之建立...……………43
§3-3 基本位相關係的演算法設計………………………………….44
§3-3-1 目前幾何演算法所面臨的問題…………………...…44
§3-3-2 基本位相關係之幾何配置分析……………………...45
§3-3-3 基本位相關係演算法的建立………………………...48
§3-4 增進實行效率的考量………………………………………….51
§3-5 結論…………………………………………………………….53
第四章 組合物體的位相關係………………………………………..60
§4-1 折線物體與基本物體間的位相關係………………………….61
§4-2 組合物體的位相關係………………………………………….73
§4-2-1 組合物體的位相關係分析與定義………...…………74
§4-2-2 組合物體與基本物體間之位相關係舉例…...………78
§4-3 空間物體的階層關係及其間的位相關係……………………82
§4-3-1 空間物體的階層關係以其應用……………………...82
§4-3-2 根據地理資料階層關係的位相關係推理…………...83
第五章 位相關係模組之測試與分析………………………………..98
§5-1 位相關係模組之架構………………………………………….98
§5-2 基本位相關係之測試…………………………………...……103
§5-3 組合物體位相關係之測試…………………...………………107
§5-4 階層關係於位相關係推演之應用…………………………...109
第六章 結論與建議…………………………………………...…….112
參考文獻…..………….……………………………………………….114

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