基础拓扑空间

With respect to syntax, the roles of tagmeme in the structure of word and sentence and Chomsky's Generative-Transformational Grammar are discussed. The spatial relation theory and existing research achievements are investigated. Having noticed the shortage of the capability of topological and metrical relation in the description of spatial information structure, the author proposes Combinational Qualitative Geometry based on the two invariables under ordinary transformations, distance ratio and direction difference, the CQG-based spatial relation system between topological and metrical constraint is thus constructed, on which several spatial relations such as parallel, perpendicularity, co-linearity, sequence and direct neighborhood are derived. Based on extended theory of spatial relation, the language anamorphosis is analyzed from the aspects of phonetics, semantics and syntax. The mere geometric and formalized spatial relation is then integrated with concrete geographic ontology to accommodate richer and indicative spatial configuration of spatial information in the different geographic context. Finally a syntax framework for spatial information is put forward.

在语法结构方面，首先阐述了法位和法素在语法结构词法和句法中的地位和作用，以及Chomsky生成转换语法的核心内容；详细介绍了地理信息系统空间关系理论及现有的研究成果；在分析现有的拓扑关系和量度关系对空间信息结构描述能力不足的基础上，提出了基于长度比和角度差两个不变量的组合定性几何，以此建立了介于拓扑及量度约束之间的组合定性关系体系，并以此为基础派生出平行、垂直、共线、次序、直接邻近等空间关系描述；本文基于扩展的空间关系理论，详细讨论了空间关系在语音、语法和语义三个方面的语言变体，将纯几何和纯形式化的空间关系与具体的地理本体结合起来，可以获得更为丰富的、更能反映空间关系在不同语言上下文中具体体现的组合关系；最后给出了一个空间信息的语法结构的基本框架。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component. For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper. For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space state informatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision. Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为（n-1）维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料（单质材料作为特殊的功能梯度材料看待）、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

This paper presents an IFMC CAD model that consits of a geometry model and a material model, in which the geometry space acts as a base space and the material space acts as a bundle space. In this CAD model, the geometry model is based on the non-manifold model. In addition, a half-face data sturucture, which is derived from the half-edge data structure with the non-manifold feature of IFMC taken into account, is adopted to represent the geometry and topology information of the component.For the material model of IFMC, this paper focuses on the FGM component representation firstly and present a simplex-subdivision based CAD data exchange format, in which the material information is represented as a (n-1) simplex and material .distributing feature is represented by the interpolation on the simplex-subdivision. Based on those, a part-building orientation optimization algorithm and an adaptive slicing algorithm for FGM component are presented in the paper.For the IFMC material model, the IFMC material information representation is divided into a meso-scale and a macro-scale representation. In the meso-scale, a concept named parameterized periodic functional meso-structure is presented as a unique form to represent the FGM (the homogeneous materials are regarded as a special FGM), the composite and the functional meso-structure material. The model of PMS is a three-tuple that contains the space stateinformatation, the material parameter and the material meso-scale distribution feature. The macro-scale material information representation is similar to the FGM components by interpolation of the control parameter of the periodical functional meso-structure based on the simplex-subdivision.Through an example of manufacturing-oriented IFMC CAD data processing, it is proved that the IFMC CAD model and the material information representation and process method proposed in this paper can provide a reliable data support for IFMC digital concurrent design and manufacturing.

本文将理想材料零件CAD模型建立在以几何空间为底空间、以材料空间为丛空间的结构上，使用非流形几何模型作为理想材料零件几何拓扑模型的基础，并在半边数据结构基础上，针对理想材料零件的非流形特征局限内部边界上的特点，给出了一个半面数据结构来表述零件的几何拓扑信息；对于理想材料零件的材料模型，本文先从功能梯度材料零件的信息表述与CAD数据交换和处理入手，将材料信息表述为(n-1)维单纯形，然后通过对三维几何区域的单纯剖分，以插值的方式表述零件材料分布特征；在此基础上，根据功能梯度材料零件分层制造中对CAD数据处理的要求，给出了综合考虑零件几何特征与材料特征的生长方向优化算法和自适应切片算法；而对于文中所定义的理想材料零件，本文将其材料信息表述分解到细观和宏观两个尺度进行，首先给出了细观尺度上参数化的周期性功能细结构概念，以此来统一表述功能梯度材料(单质材料作为特殊的功能梯度材料看待)、复合材料和功能细结构材料；把周期性功能细结构模型化为一个包含空间状态信息、材料构成参数和材料细观分布特征参数的三元组，以表达零件的细观材料特征；对于零件宏观的材料变化特征，则同样在几何区域单纯剖分的基础上，通过对细观尺度上周期性功能细结构控制参数的插值来完成；通过理想材料零件CAD数据处理的算例，验证了本文中理想材料零件CAD模型及材料信息表述与处理方法完全可以为理想材料零件的数字化制造提供可靠的数据支持。

Based on theanalysis of topology structure of parallel mechanisms and using differential topology anddifferential manifolds as mathematical tools, we propose a new classification method. Thismethod classifies singularities of parallel mechanisms into two basic types, i.e. topologysingularity and parameterization singularity. This kind of classification has clear physical andmathematical meaning and fully reveals the characteristic of configuration space of parallelmechanisms.

采用微分拓扑和微分流形等现代数学工具，在对并联机构位形空间的拓扑结构进行分析的基础上，提出了一种新的奇异位形的分类方法，即把奇异位形分为拓扑奇异位形、参数化奇异位形两种类型，这种分类方法充分体现了并联机构位形空间的特点，具有十分明确的物理和数学意义。

This paper aims at the prominent issue that current models of spatial topological relations can not represent complex object, among which 9-Intersections Model (9IM) is well known. Therefore, taking cadastral data as example, one model of topological relations between complex and spatio-temporal objects based on 9IM is put forward. And the improved sweep-line algorithm is designed. Specific studies as follows:(1)According to the concepts of point set topology, the author distinguishes the complexity of the object, redefines the spatial point, line and region. For instance, in the simple region, concave one is more complex than convex, composite regions can be composed of many parts or with holes, and so on.

本文针对当前空间拓扑关系模型无法表达复杂对象的突出问题，以地籍对象为实例，以9I模型为基础，探索了一种适合复杂对象和时空对象的拓扑关系表达模型，较好地解决了地籍对象中各类要素间拓扑关系的描述和应用，实现了地籍变更中变化语义类型的推理和历史回溯；通过对现有的拓扑关系计算方法进行了改进，设计了相关算法，给出了C语言程序示例；最后通过实验系统的实现，验证了模型和算法的可行性。

Based on concepts of relative algebraic interior and relative topological interior of sets,some conditions assuring Ari+Bri in a linear space and conditions assuring riA+Bri in a linear topological space are given respectively,according to Tanaka and Kuroiwa' s conclusions.

根据Tanaka和Kuroiwa的结论，在集合相对代数内部和相对拓扑内部概念的基础上，分别讨论了线性空间中Ari+Bri和线性拓扑空间中riA+Bri成立的条件，从而将Tanaka和Kuroiwa关于内部的结论推广到了相对内部的情形

Based on the description of uncertain linear and area objects, intersection degrees for parts of uncertain linear and area objects are represented quantitatively. By calculating correlation degrees between spatial vectors composed of these measurement units and spatial relation vectors determined by 9-intersection model, a new model is presented for topological relations between uncertain linear objects and fuzzy region, which could distinguish the type of topological relations through quantitative analysis method.

在时不确定线状目标和面状目标进行描述的基础上，对不确定线状目标与面状目标各组成部分之间的相交程度进行了定量表达，通过计算这些度量组成的空间向量与9-交集模型确定的空间关系向量之间的相关度，提出了一种不确定线状目标和面状目标之间拓扑关系的描述模型，通过定量的方法来对其空间拓扑关系进行判别。

This paper models the underlying network topology as an Euclidean space and uses PCA to map this higher dimensional space to the lower dimensional logical space of CAN. So a peer's identifier is determined by its location in underlying network.

以对等网络系统CAN为基础，将底层网络拓扑建模为高维欧氏空间，使用主成分分析法将底层网络拓扑映射到低维CAN逻辑空间，从而根据节点在底层网络中的位置决定其在对等网络中的标识符。

This representation method not only wides SRC Ontology's 8 topological relation representation method, and provides more explicit formalization representation for spatial relation ontology modeling, but also make the practical application possible.

该表示方法比SRC-Ontology 8种拓扑关系表示更适合点、直线、面三类空间目标表示的需要，为空间拓扑关系建立本体模型提供了更加清晰明确的形式化表示基础，同时使得实际应用成为可能。

Based on the profound analysis for representation and reasoning of qualitative spatial relations, this paper proceeds with some originality innovation researches as follows:(1) Representation of spatial topological relations Based on the point-set topology and ontology, representation methods for spatial topological relations are researched.

在对定性空间关系表示与推理进行深入分析的基础上，本文进行了以下几方面的创新性研究：(1)空间拓扑关系表示以点集拓扑学和本体论为基础，研究了空间拓扑关系表示方法。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。