平移

Finally, since there is no absolute origin in time, all systems must be invariant under time displacements.

最后，因为没有绝对的时间原点，所以任何系统在时间平移下一定不变。

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。

To extract shaft orbit\'s features invariant to rotation, scaling and translation, the unique strengths of Haar orthogonal matrix type are found, the horizontal and vertical coordinates of shaft orbit are fast proceeded by Haar transform, respectively, and the slopes with different resolutions are obtained at different positions by using the corresponding transform coefficients, and then the multi-resolution angles between the adjacent slope straight line are extracted skillfully and used for the hierarchical recognition, the recognition process accords with the principle of human\'s recognizing things by using hierarchy analysis approach.

为提取轴心轨迹平移、旋转、尺度不变性特征，本文挖掘出Haar正交矩阵在图形识别中的独特优点，引入Haar正交矩阵分别对轴心轨迹的横、纵坐标进行快速变换，并利用变换后的对应系数得到轴心轨迹不同位置不同分辨率下的斜率，继而推求出相邻斜率直线之间的多分辨率夹角，所获夹角用于轴心轨迹的分层识别，其识别过程符合人类识别事物层次分析的规律。

When a few of local 3D terrain models have been reconstructed respectively,firstly find the common 3D points between every two adjacent local models based on edge detection and image matching,secondly fit the matrix of coordinate transformation employing the technique of separating rotation matrix and translate vector,and lastly register these local 3D models into a single coordinate system.

当恢复出多个局部3D地形模型时，首先基于边缘检测和图像匹配技术提取出相邻局部模型之间的公共数据点，然后采用分离旋转变换和平移矢量的策略拟合出相邻模型之间的坐标转换关系，之后就可以将局部模型统一在同一个坐标系下。

We study a polygon representation composed by the vertex angles and ratios of adjacent edge lengths, which is invariant to geometric transformations such as translation, rotation and scaling. The polygon is globally represented by a scale-invariant intrinsic matrix.

提出了由顶点转角和相邻边长比例构成的多边形伸缩内在量表示的方法，多边形从整体上由一个伸缩内在矩阵来表示，该表示方法具有平移、旋转和伸缩等几何不变性。

They include:collinearity--an invariance under the projective transformation group;Parallelisminvariance under the affine transformation group;the direction of angles--aninvariance under the rotation transformation group.

这些几何不变性质包括共线性——在射影变换群下的不变性；平行性——在仿射变换群下的不变性；角的方向——在欧氏平移变换群下的不变性。

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

In affine invariant space, the 3D object is not affected by geometric transformations, such as translation, rotation and scaling.

由于在仿射不变空间下，3D物体模型不受平移、旋转和比例变换的影响，故该水印方案对于此类变化具有很强的鲁棒性。

The image registration firstly assumes that there is some transformation between frame and frame of images, such as translation, affine and planar surface etc. and then registers images.

图象配准算法首先假设图象帧间存在某些变换，例如平移变换、仿射变换和平面变换等，然后对序列图象进行运动配准。

Simulation results prove that symmetry algorithm is applicable for generating the long periodic hopping pattern used in valid data communications, while random shift replace algorithm is proper for the short periodic pattern with the good balance in the range of maximum effective length, and it can be used in the situations of short-cycle emergency communications.

仿真结果表明，对偶法在长周期条件下的性能优于随机平移法，适用于产生正常通信使用的调制跳变图案；随机平移法在最大有效周期长度范围内具有很好的均衡性，适用于短周期突发通信。

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。