平移对称

This paper illustrates the process where projective transformation and affine transformation are employed to solve advanced geometrical problems.

引言变换是我们在几何解题中常用的方法之一。初等几何中的变换方法有对称变换、平移变换、旋转变换和相似变换，高等几何中的变换有射影变换、仿射变换等。

By taking advantage of a corollary of the Desargues theorem and the corresponging extension of Desarguesian configuration, the concept of stereohomology has been defined in projective geometry and presented based on homogeneous coordinates. Consequently, a series of geometrical transformations, such as central projection, parallel projection, centrosymmetry, translation transformation, reflection, rotation transformation, which can be contained in it or derived from it have also been analytically defined.

利用Desargues定理的一个推论和引申的Desargues图形，给出"空间透射"在射影几何意义下基于齐次坐标表象的解析定义，从而解析定义了可蕴涵其中的中心投影、平行投影、中心对称、平移、反射等几何变换以及可由此衍生出的旋转变换。

The dissertation focuses on the phenomenon of wave propagation of piezoelectric periodical composite laminated plate. By using the motion equations and Gauss theorem cooperative with constitutive relations of piezoelectricity, the governing equations can be determined.

本文主要是要探讨压电周期叠层板波传现象，所以由本构方程式配合运动方程式和高斯定理以获得统御方程式，此等方程式在周期结构内具有平移对称关系，所以位移场和电位场的形式可以布拉克理论表示，进而得到代表周期结构行为的统御方程式。

I was a university student, I had not done a very complex programming exercise, This is the first time I upload source. this is the upload computer graphics, I do exercises at the WIN-TC environment prepared by some of the procedures, these are the basic 2D graphics transform (translation, rotation, Shear, Zooming, symmetric) animation demonstration, three-dimensional map of the two-dimensional plane of the hidden map, the lines cut, the parabolic mapping and B-spline curves mapping, detailed procedures of the Notes, and I hope to the students friends to help.

详细说明：我是一名大学的学生，我没有做过很复杂的编程练习，这也是我第一次上传源程序，这次上传的是我做计算机图形学的练习时在WIN-TC环境下所编的一些程序，其中有二维图形的基本变换（平移，旋转，错切，放缩，对称）的动画演示、三维图在二维平面上的消隐图的显示、线条的裁减、抛物线的绘制以及B样条曲线的绘制，程序中有详细的注释，希望对学生朋友们能够有所帮助。

Based on raw materials, this thesis begins with Escher's exploration of mathematical methods, analyzes his regular division of the plane with preliminary symmetric principles-concepts about symmetry and isometry transformation, rotation, ref...

本文基于原文资料的整理，以埃舍尔对数学方法的探索为切入点，运用数学中初步的几何原理——对称概念及等距变换概念(旋转、平移、反射、滑移反射)对埃舍尔的周期性空间分割图案进行了详实的分析，进而对艺术设计的形式中感性与理性、艺术设计与科学等关系进行探讨。

Mouse drawing,parallel translation,rotate,mirror,formula curve,list curve,gear program-package.

鼠标绘图，图标提示，可直接使用块平移、旋转、对称，公式曲线、列表曲线和齿轮软件

However, proving axisymmetry for the Onsager model is still very difficult, at least for two reasons: The first is that we lack methods for proving axisymmetry, even though there are method for proving radial symmetry or translation invariance.

但是，证明了Onsager模型轴对称仍然是非常困难的，至少有两个原因：第一，我们缺乏证明轴对称的方法，即使是证明辐射对称或平移不变性的方法。

Key Words: decimal, symmetry, translation and rotation, multiplication

重点词汇：小数，对称、平移与旋转，乘法

Geometric transformations are translation, rotation, symmetry, shear, variable ratio.

几何变换有平移、旋转、对称、错切、变比。

The first one is the system for the two-armed hard-flexible manipulators moving in a certain channel. The dynamic model of that is proposed based on the D'AlembertLagrange principle.

第一个模型研究了由两支对称的刚性-柔性机器臂构成一个双臂机器人的定轨道水平移物问题，利用D'Alembert-Lagrange原理建立了双臂钢性-柔性机器人系统的双臂机器人定轨道移动的非线性对称组合模型。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。