和向量

This is my last OpenGL for a project to use the "three-dimensional vector space / point" and related functions, they can use a definition of space vector / points, for the vector translation, zooming and rotation, the use of correlation function can also achieve two vector by the fork, get a Vectors absolute length of a vector unit, received a 3:00 decision vector perpendicular to the plane, a space to be the distance between two points, two vector to be the plot points, to be the angle between two vectors, such as operating for the use of user-friendly, each function is detailed Notes, it is particularly important if the calculation vector plot points, fork also took note, we hope to have useful.

这是我过去进行一个OpenGL项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，特别重要的向量计算如点积，叉乘还有相关说明，希望对大家有所用处。

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

Using the theories of probability, algebra and spectral theory comprehensively, we investigate some related characteristics of logic functions in cryptography: Firstly, we introduce m order generalized s - correlation immunity of Boolean vector functions and prove that the higher order generalized ε- correlation immunity can guarantee the lower order generalized ε- correlation immunity. Then by applying decomposition formula of joint distribution of Boolean random vectors, we give a spectrum criterion of m order generalized e - correlation immunity of Boolean vector functions. Furthermore, we show that the algebraic degree of m order generalized e - correlation immune Boolean vector functions is not restricted by the correlation immune orders.

本文主要运用概率论的思想和方法，并结合代数学和频谱理论的相关知识，对密码学中逻辑函数的有关性质进行了研究，主要包括以下三个方面的内容：首先，对布尔向量函数的相关免疫性进行了拓展，给出了k维布尔向量函数m阶广义ε-相关免疫的概念，证明了布尔向量函数的高阶广义ε-相关免疫性蕴含低阶广义ε-相关免疫性，并根据布尔随机向量联合分布分解式得到了布尔向量函数m阶广义ε-相关免疫的一个谱判别条件，还说明了m阶广义ε-相关免疫布尔向量函数的代数次数不受相关免疫阶数的制约。

This is a project to use the three-dimensional space vector/point type and related functions, they can be defined using a space vector/point, the realization of vector translation, scaling and rotation, the use of correlation function can also be the realization of the two vectors fork x, the absolute length of a vector, a vector unit, and get a three-point decision to the vertical plane of the vector, be the distance between two points in space, by the two vectors point multiplication by the two vectors angle, such as operations, for the use of user-friendly, each function are detailed notes, I hope all of you useless.

详细说明：这是一个项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，希望对大家有所用处。

First,by choosing a control function for a local adaptive optimal neighborhood,the filter window is set in the region with similar normals to avoid the problem of shrinkage and over-smoothing.

首先通过自适应选取最优邻域控制函数来将滤波窗口限制在顶点法向量相近的区域，以防止滤波后模型的收缩和过光顺；然后运用协方差矩阵分析的方法，在最优邻域内计算出各采样点的法向量和曲率；最后以采样点滤波参考平面为基准，分别平滑采样点的法向量和位置，即先对采样点的法向量进行多边平滑，然后根据新的法向量来多边平滑输出各采样点的位置偏移量，最后在法向方向上移动该顶点，以达到降噪的目的。

For this reason, the author of the article puts forword a new concept projective vector and coefficient "image" of projective vector. Coefficient of projective vector is put forword by the author for the frist time. It is of high value, both in mathematics and theory.

为此，本文给出了"一个向量在另一个向量方向上的射影向量和射影向量系数"的概念，"射影向量系数"这一概念，为作者本人首次提出，具有重要的教学价值和理论价值。

In principle, there are two methods of describing glyphs in fonts:bitmaps and vectors.

原则上，在字体中有两种描述符号的方法：点阵和向量。

The approach primarily adopts patch-based texture synthesis flow, synthesizing progressively-variant textures to reflect the diversification trend of vector fields.

在纹理合成过程中利用向量场作为指导，生成反映向量场大小和方向变化的合成结果·采用块纹理合成的流程，在对向量场合成块均匀划分的基础上，通过进一步的自适应分割，将向量场划分成为不同大小和不同形状的最终合成块，使之与向量场的变化趋势相吻合·对向量变化过于剧烈的区域，则采用点合成的方式进行纹理合成，以保证合成效果的平滑·实验表明，文中的方法可以实现快速而高质量的向量场可视化

As with vectors, reading more than one matrix component is called swizzling.

和向量异向，读取多个矩阵通道叫做 swizzling 。

It is equivalent to the vector cross-product, and returns a vector quantity only

它和向量叉积等价，并且只返回一个向量值

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。