几何基础

词组短语

foundation of geometry · foundations of geometry

与几何基础相关的网络例句 [注：此内容来源于网络，仅供参考]

Based on the three dimensional surface data of the face and skull, methods of geometric analysis on them are presented through these parameters with their numerical calculating methods under the landmarks of the anthropologist and anthropometrist are proposed,which is the foundation of the statistical model that will be used in the field; 4Geometric analysis methods that based on the approximation coefficients of spherical harmonic functions are proposed.

以三维面皮和颅骨数据为基础，分别给出了基于公安法医学标志点和人体测量学标志点的几何分析主要途径和方法，确定了几何分析的主要参量，并给出了相关的计算方法，为建立颅面统计模型奠定基础； 4基于球面调和函数的颅面形态学的几何分析方法。

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 projective geometry,the research works about 3D invariances extraction and application have been done in this thesis as following:(1) The basic theories and concepts in projective geometry are systematically summarized. It includes:the camera models of perspective imaging,projective collineation,cross ratio,a simple compare about invariance among some geometry transformations,fundamental matrix,epipolar and epipolar line in epipolar geometry,and so on.

基于射影几何理论，论文围绕3D不变特征的提取和应用进行了如下的研究工作：(1)系统总结了射影几何中的若干基础概念，包括：透视成像的相机模型、射影对应、交比不变量、基于不同几何变换下的不变量的简单对比、对极几何中的基础矩阵、对极点、对极线等。

Based on projective geometry, the research works about 3D invariance's extractionand application have been done in this thesis as following:(1) The basic theories andconcepts in projective geometry are systematically summarized. It includes: the cameramodels of perspective imaging, projective collineation, cross ratio, a simple compare aboutinvariance among some geometry transformations, fundamental matrix, epipolarand epipolar line in epipolar geometry, and so on.

基于射影几何理论，论文围绕3D不变特征的提取和应用进行了如下的研究工作：(1)系统总结了射影几何中的若干基础概念，包括：透视成像的相机模型、射影对应、交比不变量、基于不同几何变换下的不变量的简单对比、对极几何中的基础矩阵、对极点、对极线等。

Conventional flow mathematical models of coalbed methane are all based on Euclidean geometry.

传统的煤层气渗流数学模型均是建立在欧几里德几何基础上的。

In the fourth chapter, I analyze and contrast many architectural cases in history and modern times which ellipse were applied to, and explore the ellipse"s development in historic sense. The fifth chapter investigates the dynamic relationship between geometry and architecture based on ellipse"s geometric character, and analyzes ellipse architecture"s characters in symbolism, dualism, diversity and unity these four facets. In the sixthchapter, taking ellipse architecture as examples, I try to explore the relationship between the more general geometry"s purity and architecture"s complexity, and build the foundation for future exploration of geometry"s purity.

第四章从历史和现代两个方面展开了大量对椭圆形式在建筑中应用的个案和实例的研究与对比，探讨了椭圆形式在历史上意义的变迁；第五章以椭圆的几何特性为立足点，研究了椭圆几何--建筑之间的动态关系，从标志性，二元对立，多样和统一四个方面分析了椭圆建筑的特点；第六章以椭圆建筑为例，尝试探讨了更一般的几何的纯粹性与建筑的复杂性的关系，对几何纯粹性意义的挖掘为进一步的研究提供基础；第七章采用了类型对比的研究方法，分析了安藤忠雄和库哈斯两位设计哲学截然不同的建筑师对椭圆形式的使用；另外，以位置关系为线索，将椭圆和其他的几何形式结合起来，总结了一般情况下几何的纯粹性对建筑复杂性的作用。

Gauss assigned to Riemann the subject of the foundations of geometry as the one on which he should deliver his qualifying lecture.

Gauss 给 Riemann 指定把几何基础作为他应该发表的就职演说的题目。

In order to explore solutions to the problem, so the sample students learn to socialist modernization, and further Xuexi Suobi Xu of algebraic, geometric probability and basic knowledge and a rudimentary micro-integration, and forms the basic skills; further developing of thought Nengli , computing power, spatial imagination, the ability to solve practical problems and sense of innovation, from last year, to understand the science ...

为了探索解决问题的办法，使学生在高中阶段学好从事社会主义现代化建设和进一步学习所必需的代数、几何基础知识以及概率统计和微积分的初步知识，并形成基本技能；进一步培养学生的思维能力、运算能力、空间想象能力、解决实际问题的能力和创新意识，从去年起，为了解学。。。本文共有6999字

First, geometric basis of nonlinear control is introduced.

首先，本文介绍了非线性控制的几何基础。

与几何基础相关的网络解释 [注：此内容来源于网络，仅供参考]

Linear Algebra：线性代数

>(Linear Algebra)是教育部工科数学教学指导委员会列出的重点基础理论课之一,线性代数起源于欧氏几何、线性方程组理论、解析几何. 例如,线性方程组的系数和常数项按其顺序排列就得到矩阵,齐次线性方程组的解在加法和数乘下是封闭的,

bevel gear：锥齿轮

由于锥齿轮 ( Gear ) 沿齿宽方向截面大小不等,引起载荷沿齿宽方向分布不均,其受力和强度计算都相当复杂,故一般以齿宽中点的当量直齿圆柱齿轮 ( Spur Gear ) 作为计算基础. 一、直齿锥齿轮 ( Bevel Gear ) 传动的当量齿轮 ( Gear ) 的几何关系

Cheating：作弊

芒德勃罗回忆说,当时他的代数与分析基础并不好,但几何直觉不错,考试 时他总是设 法将代数与分析问题化成几何问题,巧妙地将它们解决,他称此为合法性"作弊 "(cheating).

Commutative Algebra：交换代数

基础代数 Fundamental Algebra | 交换代数 Commutative Algebra | 代数几何 Algebraic Geometry

Computational Geometry：计算几何

它的主要数学理论基础即为计算几何(Computational Geometry),由函数逼近论,微分几何、代数几何、计算数学、计算机图形学等形成的. 与UG、I-DEAS、EUCLID、PRO/ENGNEERING等现在流行软件相比,该软件在曲面造型方面具有其独到的数学准确性的特点.

Descriptive Geometry,Shadow and Perspective：画法几何与阴影透视

互换性与技术测量实验 Experiment of Exchangeability Measurement Technology | 画法几何与阴影透视 Descriptive Geometry,Shadow and Perspective | 化工基础 Elementary Chemical Industry

Differentiable Manifolds：微分流行

微分几何 Differential Geometry | 微分流行 Differentiable Manifolds | 微观经济学基础 Fundamentals of MicroEconomics

foundation of geometry：几何基础

foundation 基础 | foundation of geometry 几何基础 | foundations of geometry 几何基础

foundations of geometry：几何基础

任何人都会知道欧几里得的>、笛卡尔的>(Geometry)与希尔伯特(HilBert)的<<几何基础)(Foundations of Geometry)都是数学的书,彼此多少和同一个主题相关.

geometrical optics：几何光学

最初,人们从物体成象的研究中形成了光线(1ight ray)的概念,并以光的直线传播性质为基础,总结出了光在透明介质中的反射和折射的规律,逐步形成了几何光学(geometrical optics).