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In practice, the offset curve usually is approximated by lower degree rational polynomial cur ve in order to have the unified expression of data structure and geometric algor ithm in the commercial modeling systems.

通过用双圆弧逼近表示 NURBS( non- uniform rational B- spline)曲线及其 offset，并利用双圆弧逼近的特有性质，把 offset的双圆弧逼近转化为原曲线的双圆弧逼近，简化了问题的求解。

For CVFE grid, the reduced pressure is approximated using finite element method and a new upstream weighting approach is proposed, which are more accurate and reasonable.

用这种方法得到的三角形满足Delaunay条件，得到的非结构网格是最优的。

Veidt hovered through a quarter turn to face him with what nearly approximated a smile.

维特转过四分之一圈，带着一种类似微笑的表情看着他。

This paper reviews the control theories used for robot in details. The interative and nonlinear torques of the traditional robots at the joint axis are reduced by a factor of gear ratio. The complicated arm dynamics is approximated to a linear, time-invariant model. The robot can be controlled by using local, decoupled PID's controller at each joint.

本文对机器人控制理论进行了全面综述，指出对于常规机器人，由于减速机构的存在，其耦合力矩和非线性力矩被大大减弱，其动力学模型可近似为线性、定常、解耦模型，采用独立关节PID控制即可。

In order to obtain more exact analytical solution to study the output characteristics of double-clad fiber lasers,according to the continuous-wave rate equations of fiber lasers,using typical parameters of double-clad fiber lasers,the contribution of the re-emission effect arising from the interaction between the upper-level atoms and pump light was estimated.Taking into account the predominant part of the re-emission to improve the accuracy of the integration approximated rate equations,the integration of the product of the loss and radiation should be found and explicit analytical expressions for the output of the DCFLs and gradient efficiency of the pump radiation,were deduced,and certain issues of concern were discussed.

为了求得用于研究双包层光纤激光器输出特性的更为精确的解析解，根据稳态速率方程组，针对典型的双包层光纤激光器参量，在估计了上能级粒子再发射项和抽运光产生的影响后，采用保留再发射贡献主导部分的办法以提高可积分近似方程的精确度，明确地提出了要获得光纤激光器输出功率的解析表达式的关键在于求出损耗系数与光场乘积的积分值，简洁地求得了输出功率和抽运光斜线效率的显函数解析表达式，并对其相关问题进行了讨论，以915nm，920nm和975nm的抽运光为例，当输出激光为1090nm时，得出975nm抽运光产生的斜率效率最高并可高达约87%。

A content based adaptive mesh generation algorithm is proposed in this paper. At first, a watershed algorithm of mathematical morphology is used to segment image into many homogeneous regions so that watershed lines can better represent image structure, contours, and edges. Boundaries of these regions are approximated by polygons that can be represented with a few parameters. Each end point of polygonal sides serves as candidate node of mesh model.

文中提出的基于图像内容的自适应网格模型生成算法，首先利用数学形态学中的水线算法把编码图像分割成许多纹理一致的区域，所分割的区域反映了图像的结构、轮廓和边界；再对这些区域的边界进行多边形拟合，得到多边形各个边的端点作为网格模型的节点，以这些节点为基础就能生成一个 Delaunay 三角形网格。

RCBV values calculated using cSVD and oSVD were identical. Both values were equal to the whole areas under the concentration-time curve were divided by the arterial input function areas. Moreover, these rCBV approximated to the rCBV calculated by signal-time curve fitting. rCBF with cSVD and oSVD wouldn't be underestimated by delay effect and were good for relative quantity. The scatter plots of rMTT and Td were useful in stroke staging.

cSVD和oSVD所得组织脉冲反应曲线的面积相等，均等於完整的浓度时间曲线下面积除以动脉输入函数下全部面积；而且，此结果和讯号时间曲线拟合很接近。cSVD和oSVD不会因延迟效应低估rCBF，可以良好反应不同组织的血流量相对值。rMTT和Td散布图在不同疾病种类或处於不同疾病分期，显示不一样的分布。

For observers near the central line of a total eclipse, the limb corrections can be more closely approximated by using a smaller value of k, which accounts for the valleys along the profile.

对于全食中心线附近的观测者而言，使用较小的K值进行边缘修正更合适。

When the IAU's value for k is used to calculate these times, they must be corrected to accommodate low valleys or high mountains along the Moon's limb. The calculation of these corrections is not trivial, but is necessary, especially if one plans to observe near the path limits (Herald 1983). For observers near the central line of a total eclipse, the limb corrections can be more closely approximated by using a smaller value of k, which accounts for the valleys along the profile.

当IAU的K值被用来计算这些时刻，他们必须纠正并使其符合月球边缘的低谷和高山，这种修正并不是不重要的，相反是很必要的，特别是计划观察靠近极限路径时（Herald 1983），对于靠近全食中心线的观测者来说，在使用更小K值的情况下，边缘修正会被更准确地近似，这个K值代表山谷沿着轮廓。

A smooth approximation algorithm is then proposed based on hinge-finding algorithm via curved faces approximated to the hinging hyperplanes model, which can obtain a smooth approximation result and hold some good properties of hinge-finding algorithm such as simplicity and effectiveness.

本文对找链接算法做了两点改进，其一是扩充了链接超平面模型，在二维空间上弥补了链接超平面模型表示能力不足这一弱点。仿真实验显示使用扩充后的模型得到了更好的分片线性逼近结果。另一点改进是使用双曲光滑函数构造出了基于找链接算法的光滑逼近算法。理论分析证明了算法的可行性。仿真实验验证了理论分析。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。