几何形状

The book is structured so that the reader may choose parts of the text to read and still take away a completed picture of some area of differential geometry Beginning at the introductory level with curves in Euclidean space, the sections become more challenging, arriving finally at the advanced topics which form the greatest part of the book:transformation groups, the geometry of differential equations,geometric structures, the equivalence problem the geometry of elliptic operators, G-structures and contact geometry.

这本书是结构，以便读者可以选择部分文本阅读，还带了一个完整的画面，有些地区的微分几何开始入门级和曲线的部分，在欧氏空间变得更有挑战性，终于到达了高级的主题，形成了最大的一部分书：变换团体、几何的微分方程、几何结构、等价问题的几何形状，G-structures椭圆算子和接触几何。

Fractals are complex geometric shapes that have been studied by mathematicians since the 1970s.

不规则碎片形是一种复杂的几何形状，自上世纪70年代起，数学家们一直在对这种几何形状进行研究。

Space curve is one of the basic elements in geometric modeling, and its effective representation is the basis of modeling. Parametric representation based on features is a kind of high-level representation including semantic information. In Chapter 4, para- metric representations based on features for free form space curve are investigated, and a parametric model for the loop of plain knitted fabric is established, in which 5 parameters with practical meanings are used to represent the shape of a loop and the relationship between loops. A new shrinkage prediction method for knitted fabric are proposed based on the parametric representation and energy minimizing. Experimental results on some plain knitted fabrics illustrate the feasibility of the proposed method.

空间曲线是造型中最基本的几何元素之一，对其有效的表示是造型的基础，而特征参数化表示是其中一种包含语义信息的高层次表示，本文对空间自由曲线的特征参数化表示进行研究，建立了一种针织物线圈的特征参数化几何模型，采用5个具有实际意义的参数表示织物线圈的几何形状及线圈之间的位置关系，并将该模型与能量极小化的方法相结合，得到了一种能较好地预测针织物缩水率的新模型，对随机选取的一些针织布缩水预测实验表明了算法的可行性。

In this paper, through an imaging system , the planar image of the inner sur- face of a pipe is obtained, and the judging creteria of analogy between object and image is given. Then, the geometric shapes of images of planar mirror ,conemirror ,off- axis spherical mirror are analysed in detail .

对管道内表面，通过成像系统在乎面上成像，给出其物像之间几何形状相似的判定标准，并对平面反射镜、圆锥反射镜和离轴球面反射镜在平面上成像的几何形状进行了详细的分析。

But the better synthesized ability of the reducing vibration and noise, bending resistance of the different stiffener section forms is the key problem concerned for by engineers.

由于筋的几何形状种类繁多，究竟那一种几何形状的筋抗振、降噪和弯曲应力等综合指标最好是工程技术人员所关心的问题。

After verification of the program, the mathematical models of the suspension bridges were studied by means of the program, as well as the determination of the main cable's shapes and its internal forces at different stages, the calculation of the cable's unstrained length and the analysis of the construction processes, of which some new approaches were presented in the mean time. Thus makes the structural analysis results of suspension bridges more reliable and in accordance with reality.

在用算例验证了程序分析结果正确性的基础上，应用该程序对悬索桥的数学模型、各阶段缆索几何形状及内力状态的确定以及缆索无应力长度的计算和施工过程分析进行了研究，提出了确定缆索在成桥状态下的几何形状及其内力状态以及缆索无应力长度计算的新方法，使悬索桥的结构分析结果更加符合实际情况。

The algorithm onwhich the adjustment parameters can be worked out according to the geometricparameters of the chamfering is derivated.

影响平面尖角几何形状的是刀具的姿态参数，影响尖拱圆角几何形状的是刀具的位置参数和刀刃圆弧半径。

According to the wire electrode on the trajectory of the different forms of control, WEDM can be divided into three types:* is a copy-control, cutting their lines in advance to create the shape of the workpiece and the same mode *, When the rough machining parts and die at the same time * Clamping in the machine tool table, in the process of cutting wire electrode tightly * close to the edge of model for mobile track, thus cutting out the model * with the same shape and precision to work; another One is the optical tracking control, the cutting in line before the first parts in accordance with drawings by a certain ratio of enlarge depicts an electro-optical tracking maps, drawings will be processed when the machine electro-optical tracking placed on the stage, followed on the stage The first photo has to follow the ink line graphics track movement, and then through the use of electrical, mechanical linkage to control the machine tool table work together with the relative electrode wire Xiang Sixing do sports in order to cut out the pattern and shape of the workpiece to the same; a re - Is a digital process control, advanced digital automatic control technology, machine-driven process in accordance with the geometry of the workpiece before the parameters of good pre-processing CNC automatic completion of the processing, production do not look like without drawing board also plans to enlarge, in front of more than two Control in the form of higher precision processing and broad scope of application, at home and abroad for more than 95% of WEDM have been using digital technology.

根据对电极丝运动轨迹的控制形式不同，电火花线切割机床又可分为三种：一种是*模仿形控制，其在进行线切割加工前，预先制造出与工件形状相同的*模，加工时把工件毛坯和*模同时装夹在机床工作台上，在切割过程中电极丝紧紧地贴着*模边缘作轨迹移动，从而切割出与*模形状和精度相同的工件来；另一种是光电跟踪控制，其在进行线切割加工前，先根据零件图样按一定放大比例描绘出一张光电跟踪图，加工时将图样置于机床的光电跟踪台上，跟踪台上的光电头始终追随墨线图形的轨迹运动，再借助于电气、机械的联动，控制机床工作台连同工件相对电极丝做相似形的运动，从而切割出与图样形状相同的工件来；再一种是数字程序控制，采用先进的数字化自动控制技术，驱动机床按照加工前根据工件几何形状参数预先编制好的数控加工程序自动完成加工，不需要制作模样板也无需绘制放大图，比前面两种控制形式具有更高的加工精度和广阔的应用范围，目前国内外95％以上的电火花线切割机床都已采用数控化。

Wire electrode based on the trajectory of the different forms of control, WEDM can be divided into three types: one is shaped by the imitation controlled cutting in line in advance and work to create the same shape by mold, when processing the workpiece at the same time rough and on the mold clamping in the machine tool table, in the process of cutting wire electrode tightly against the mold on the edge of the track for the mobile, thus cutting out and die on the same shape and precision to the workpiece; another One is the electro-optical tracking control, to carry out the cutting line, before the basis of certain parts to enlarge the proportion of drawings depicts an electro-optical tracking map-processing machines will be placed in design stage of electro-optical tracking, tracking platform Photoelectric first line of graphics has always been to follow the track of the Mexican campaign, and then through the use of electrical, mechanical linkage to control the machine tool table, together with the workpiece so相似形wire electrode relative movement, thus cutting out the same shape and design to the workpiece; again a digital control, the use of advanced automatic control of digital technology-driven machine tool in accordance with the pre-processing parameters according to the workpiece geometry pre-processing procedures for the preparation of a good CNC auto-complete processing, the production does not require appearance on board the need to map to enlarge map of the previous two form of control has a higher machining accuracy and a broad range of applications, both at home and abroad more than 95% have adopted WEDM NC.

根据对电极丝运动轨迹的控制形式不同，电火花线切割机床又可分为三种：一种是靠模仿形控制，其在进行线切割加工前，预先制造出与工件形状相同的靠模，加工时把工件毛坯和靠模同时装夹在机床工作台上，在切割过程中电极丝紧紧地贴着靠模边缘作轨迹移动，从而切割出与靠模形状和精度相同的工件来；另一种是光电跟踪控制，其在进行线切割加工前，先根据零件图样按一定放大比例描绘出一张光电跟踪图，加工时将图样置于机床的光电跟踪台上，跟踪台上的光电头始终追随墨线图形的轨迹运动，再借助于电气、机械的联动，控制机床工作台连同工件相对电极丝做相似形的运动，从而切割出与图样形状相同的工件来；再一种是数字程序控制，采用先进的数字化自动控制技术，驱动机床按照加工前根据工件几何形状参数预先编制好的数控加工程序自动完成加工，不需要制作靠模样板也无需绘制放大图，比前面两种控制形式具有更高的加工精度和广阔的应用范围，目前国内外95%以上的电火花线切割机床都已采用数控化。切割属电加工范畴，是由前苏联人发明的，我国是第一个用于工业生产的国家，当时由复但大学和苏州长风机械厂合作生产的这是最早的机型叫复旦型，我们国内在此基础上发展了快走丝系统。欧美和日本发展了慢走系统LS

Based on target electromagnetic scattering and scattering centers, a matching identification method of target quasi-gemetry shape is proposed.

基于目标的电磁散射和散射中心的理论，提出了目标的似几何形状的概念，并给出了似几何形状匹配的目标识别算法。

We have no common name for a mime of Sophron or Xenarchus and a Socratic Conversation; and we should still be without one even if the imitation in the two instances were in trimeters or elegiacs or some other kind of verse--though it is the way with people to tack on 'poet' to the name of a metre, and talk of elegiac-poets and epic-poets, thinking that they call them poets not by reason of the imitative nature of their work, but indiscriminately by reason of the metre they write in.

索夫农 、森那库斯和苏格拉底式的对话采用的模仿没有一个公共的名称；三音步诗、挽歌体或其他类型的诗的模仿也没有——人们把&诗人&这一名词和格律名称结合到一起，称之为挽歌体诗人或者史诗诗人，他们被称为诗人，似乎只是因为遵守格律写作，而非他们作品的模仿本质。

The relationship between communicative competence and grammar teaching should be that of the ends and the means.

交际能力和语法的关系应该是目标与途径的关系。