坐标系的

MGM is introduced to solve field distributions in 3-D electron optical systems. The difference equation, the discrete form of Laplace's equation, is deduced in 3-D Cartesian coordinates. In view of the smooth effect, MGM combines Gauss-Seidel iteration with a technique known as coarse grid correction. Formulae for restriction and prolongation are deduced and expressed in terms of tensors.

将多重网格法引入电子光学系统中三维静电场的计算，对三维笛卡尔坐标系中的差分方程，采用高斯-赛德尔迭代法求解差分方程组，并结合迭代过程讨论了粗网格的误差校正技术；在不同网格层之间进行场值的限制和延拓，推导了三维静电场中的限制、延拓公式并以张量的形式表示。

The abscissa at the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system, the arc being of length x and measured counterclockwise from the point(1,0) if x is positive or clockwise if x is negative.

余弦以笛卡儿坐标系原点为圆心的单位圆的圆弦端点的横坐标，弧的长度为x，如果x为正，弧的长度则从（1，0）点按逆时针方向算起，若x为负，则按顺时针方向从（1，0）点算起

The abscissa at the endpoint of an arc of a unit circle centered at the origin of a Cartesian coordinate system,the arc being of length x and measured counter clockwise from the point(1,0)if x is positive or clockwise if x is negative.

余弦以笛卡儿坐标系原点为圆心的单位圆的圆弦端点的横坐标，弧的长度为x，如果x为正，弧的长度则从(1，0)点按逆时针方向算起，若x为负，则按顺时针方向从(1，0)点算起

The system gets two image of one object with two CCD, thus obtains depth from two CCD"s parallax. After investigating the operation spot and discussing with surgeons we use LED as markers, and get the marker"s 3-D position with a non-contact optics orientation method. After calibrating the CCD, processing the image, the system can figure out marker"s areal coordinates, get marker"s 3-D coordinate in dummy world coordinate system, thereby obtain instruments 3-D position and orientation. After the coordinate transformation and a series of orientation calculation, operation navigation comes true.

运用两个摄像机对同一目标从不同位置成像，进而从视差中恢复距离；通过对手术现场的仔细了解与手术医师的反复商榷，使用LED作为标志点，利用非接触式光学定位方法提取空间点位置信息：通过对摄像机的标定、图像处理及目标点重心的计算，求出空间点在虚拟世界坐标系下的三维坐标，从而确定了手术器械等的空间位姿，通过空间坐标转换及一系列定位计算，完成了手术导航实验系统。

By the circular current symmetry characteristic,on the basis of Biot-Savart law,the expression of the whole-space magnetic induction intensity distribution was deduced in the spherical coordinates system.

在球坐标系中，由磁感应强度的计算公式毕奥-萨伐尔定律出发，利用圆电流磁场的对称性推导出全空间磁感应强度B分布公式，讨论了圆电流平面上和中心轴线上的磁场，应用C数值计算方法对全空间磁感应强度B公式求解，绘制出磁感应强度分布的主要区域及磁场的空间分布图，并对全空间磁感应强度B分布特点进行了讨论。

In this research, the plane 2D mathematical model under Cartesian coordinate system and the

首先建立了直角坐标系正交网格下的平面二维数学模型及复杂边界适体坐标条件下的三维紊流数学模型，对方程的离散差分格式、控制方程的求解、初始边界条件、动边界处理等问题进行了分析研究，并编制相应的计算程序。

Vector mainly in plane geometry, Cartesian coordinate system, trigonometric functions, such as knowledge-based, learning through Vector, on the one hand, our mathematical expression of understanding entered a new field, on the other hand will enhance our space imagination capacity, the ability of thinking and analysis, the ability to solve practical problems.

向量主要以平面几何，直角坐标系，三角函数等知识为基础，通过向量的学习，一方面将我们对量的数学表达式的认识进入到一个新的领域，另一方面将增进我们的空间想象能力，思维能力和分析，解决实际问题的能力。

Special solutions for the ring circular domain with crack surfaces acted on uniform compressive force, linear compressive force and linear shearing force are deduced in polar coordinate employed the eigenfunction expansion technique in the Hamiltonian system of elastic mechanics. Combined with the general solution for the above problems, the analytical solutions for crack tip fields with surfaces acted on the above three kinds of loads are obtained. These solutions offer theoretical basis to construct analytical elements for plastic analysis of crack.

从弹性力学哈密顿体系理论出发，利用平面弹性力学极坐标系下的本征向量展开求解，推导了环形圆形域裂纹边作用有均布压力、线性压力和均布剪切力情况下的特解，从而得到了裂纹表面作用有以上三种荷载情况下的裂纹尖端场的解析解，为进一步构造进行弹塑性裂纹分析的奇异解析元奠定了理论基础。

First,the convex hull points of the characteristic region such as eyes,mouth etc. are confirmed,and,the integral contour points are obtained by fitting the curve.Then,the coordinate of the contour and the corresponding points of the adapted facial model are transformed to a new coordinate.At last,the model is adjusted in the new coordinate to get a good adaptation between the human facial model and human face image by revising the corresponding detail data in the model.

首先，对检测出的眼睛、嘴巴等特征区域，确定出其外凸包点集，通过曲线拟合得出其完整外轮廓，然后对此轮廓点以及已经粗调的对应模型点进行坐标转换，在转换后的坐标系中，对模型中相应的细节数据进行修改，实现模型和人脸图像的配准。

In the cylindrical coordinates, the related basic formula and solve method of the equivalent boundary element method were established and derived, and a new contact element was introduced to model the hybrid of structure and soil.

同时建立并推导了在柱体坐标系下插入式大圆柱壳墩式结构的等效边界元数值分析的相关基本方程和求解方法，并提出了一种新的接触面单元以模拟结构和土体间不同材料的耦合关系。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。