查询词典 geometry

As we all known, with the founding of Euclidean geometry in ancient Greece, with the development of analytic geometry and other kinds of geometries, with F.Kline" s Erlanger program in 1872 and the new developments of geometry in 20th century such as topology and so on, man has developed their understand of geometry. On the other hand, Euclid formed geometry as a deductive system by using axiomatic theory for the first time. The content and method of geometry have dramatically changed, but the geometry curriculum has not changed correspondingly until the first strike from Kline and Perry" s appealing.

纵观几何学发展的历史，可以称得上波澜壮阔：一方面，从古希腊时代的欧氏综合几何，到近代解析几何等多种几何的发展，以及用变换的方法处理几何的埃尔朗根纲领，到20世纪拓扑学、高维空间理论等几何学的新发展，这一切都在不断丰富人们对几何学的认识；另一方面，从欧几里得第一次使用公理化方法把几何学组织成一个逻辑演绎体系，到罗巴切夫斯基非欧几何的发现，以及希尔伯特形式公理体系的建立，极大地发展了公理化思想方法，不管是几何学的内容还是方法都发生了质的飞跃。

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。

On the base of these, and the ideas of mathematical curriculum reform and the course of the reform of solid geometry, combining with educational reality and students" psychology, put forward some thoughts about solid geometry of middle school in future:(1) The arrangement of curriculum content should. give consideration to both the logical sequence of knowledge and the development of students" psychology, and make them united;(2) Paying great attention to the analogy of plane geometry and solid geometry;(3) Some respects remained to be strengthened about solid geometry in senior middle school;(4) Emphasizing the importance of conversion in solid geometry;(5) Stressing on the combination of solid geometry and algebra and other subjects;(6) The design of the content of solid geometry should have certain elasticity, and make solid geometry and modern education technology well combined.

在此基础上，又植根于近年来我国数学课程改革的理念和立体几何课程改革的进展，并结合我国的教育实际与学生心理，对未来中学立体几何课程的设胃提出若干思考：(1)课程内容的编排，要兼顾知识的逻辑顺序和学尘的心理发展相统一；(2)重视平面几何和立体几何的类比；(3)高中阶段立体几何有待加强的几个方面；(4)强调变换在立体几何中的重要性；(5)注意将立体几何和代数及其他学科相结合；(6)立体几何内容的设计要有一定的弹性，并注意与现代教育技术相结合。

During the course of the well-known "new mathematics" campaign, the status of Euclidean geometry was completely overthrown in I960" s. After deeply thought of "new mathematics", the standpoint that geometry curriculum should reflect the content and method of modern geometry and be in touch with the student" s real life was agreed on. Other countries have tried some significant attempts. We can find from some geometry textbooks that the methods of transform and vector have appeared as a normal part. Simultaneous, not only the new developments of geometry such as Topology have been referred , but also the connection between geometry and practice has been strengthened.In China, geometry curriculum is also in the during of innovation.

而学校几何课程在二千年的时间里一直没有多大的变化，直到二十世纪初"克莱因—培利运动"的第一次冲击，到60年代"新数学"运动的全盘改革，以及之后的深入反思，中学几何课程要反映现代几何学的内容和方法以及紧密联系于实践的观点已经受到普遍的重视，国外的几何课程已经在这方面做了不少有意义的尝试，从国外的一些几何教材中可以发现：变换、向量等工具已经作为正式的内容进入几何教学，拓扑学等几何的新发展也开始在教材中有所体现；几何课程与实践之间的联系更是在很大程度上得以加强。

This option is not suitable to only set the startup screen (and not also the fullscreen screen), geometry is the best that is available for that purpose currently.

该选项不适用于仅仅设置启动屏幕（因为其总是在指定的屏幕上以全屏方式显示），geometry 是目前可用于此目前的最好选项。

The geometry of closing is merely scientific jargon for the fact that when the hand closes to form a fist, all fingers touch the palm of the hand at the same time.

的解释。&geometry of closing &仅仅是一个科学术语，来描述当手握紧形成一个拳头，所有的手指都会同时接触到手掌的现象。

Section 2.2 Geodes and Geometry briefly describes OSG's default world coordinate system orientation.

2.2节Geodes和Geometry已经简要的介绍过了OSG的系统默认坐标。

Section 2.2 Geodes and Geometry briefly describes OSG's default world coordinate system orientation.

2.2节Geodes和Geometry已经简要的介绍过了OSG的体系默许坐标。

As Chapter 1 explains, the cull traversal stores references to geometry and state in a render graph for processing during the draw traversal. The osgViewer library supports many threading models, some of which run the cull and draw traversals in one or more threads.

如第一章中所说的，拣择遍历包含了在一个绘制遍历时衬着图形中对于geometry和state的引用。osgViewer库撑持多线程模型，此中包括单or多线程的拣择遍历及绘制遍历。

As Chapter 1 explains, the cull traversal stores references to geometry and state in a render graph for processing during the draw traversal. The osgViewer library supports many threading models, some of which run the cull and draw traversals in one or more threads.

如第一章中所说的，拣选遍历包含了在一个绘制遍历时渲染图形中对于geometry和state的引用。osgViewer库支持多线程模型，其中包括单or多线程的拣选遍历及绘制遍历。

But in the course of internationalization, they meet with misunderstanding and puzzlement.

许多企业已经意识到了这一点，但在国际化的进程中，仍存在一些误区与困惑。

Inorder toaccomplish this goal as quickly as possible, we'll beteamingup with anexperienced group of modelers, skinners, and animatorswhosenames willbe announced in the coming weeks.

为了尽快实现这个目标，我们在未来数周内将公布与一些有经验的模型、皮肤、动画制作小组合作。