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In this paper,the rational approximation of the offset curve of Bézier curves is obtained when a polynomial of symmetric power basis is used to approximate the norm of parametric speed of Bézier curves.

等距曲线逼近技术的关键在于参数速度的逼近，文章用S幂基多项式逼近平面Bézier多项式曲线的参数速度模长，得到Bézier多项式曲线的等距曲线的有理逼近曲线，所得有理多项式逼近曲线与等距曲线在端点处能够达到高阶插值。

As for the parametric space calculation to find an optimal 3D point, the Tangent Vector Inversion is presented so as to cut down iteration.

针对求解曲面上最优点的参数域反算问题，引入了切矢逆求方法，可使迭代次数大为降低。

Design for Manufactory ; Design for Yield ; Parametric Yield ; Global Disturbance ; Tolerance Region ; Acceptability Region ; Uniform Sampling ; Uniform Design for Experiment ; Normal Distribution ; Response Surface Modeling

国家高技术研究发展计划(863计划)；教育部科学技术研究项目可制造性设计；成品率设计；参数成品率；全局扰动；容差域；可接受域；均匀抽样；均匀试验设计；正态分布；响应表面模型

And then, by regarding the curve and surface as a map from differential manifold to topological manifold, we present the framework of GRPCS and discussed its basic properties in detail. GRPCS provides a unified framework for parametric curve and surface.

然后通过势函数来构造微分流形上的单位分解，将曲线曲面看作微分流形到拓扑流形的映射，给出了广义有理参数曲线曲面的整体理论框架，并对广义有理参数曲线曲面的基本性质进行了讨论。

The following central point within a small local region of current tracing point can be obtained based on the influence of neighboring points as well as the smoothness and fairness principle. Finally, a sequential of central points can be traced out efficiently without any iteration and a parametric curve can be reconstructed by interpolating the central points.

该方法仅从当前跟踪点的邻近点集与曲线重建光顺准则出发，无须迭代，可快速、有效地跟踪得到无序点集的一个中轴点列，最后再由此点列拟合出参数曲线。

This work presents the parametric equations of acceleration poles and the polynomial equations for the loci of acceleration poles of the couplers of two planar linkages. Moreover, the design procedures for synthesizing the mechanisms with a coupler point tracing through two acceleration poles are proposed.

本论文之目的，在於推导两型平面连杆机构耦杆的加速度极心位置之参数式，及其轨迹之多项式方程式，并且分别提出设计程序，藉以合成耦杆点通过两个加速度极心之机构。

For a given mechanism, the coupler points passing through two acceleration poles are the double points on the loci of acceleration poles described on the coupler plane. Furthermore, the two mechanisms with a coupler point tracing through two acceleration poles are synthesized by utilizing the derived parametric equations.

接著，利用耦杆平面之加速度极心轨迹的交点，作为机构中可通过两个加速度极心的耦杆点，并且配合已推导出来之参数式，合成通过两个加速度极心的机构。

Parametric transversality and some applications.

Sard定理，参数横截性及应用。

Based on the review of progress in parametric uncertainty nonlinear system control theory, it is noticed that design methods based on feedback linearization are the main parts and the author proposes a robust controller design method for a nonlinear parametrization uncertain system satisfying feedback linearization and triangularity conditions,and a robust output tracking controller for a nonlinear parametrization uncertain system based on the identification of uncertain parameters.

在对该领域研究进展分析的基础上，针对满足三角形条件和反馈线性化条件的非线性参数化不确定系统提出了一种鲁棒控制器设计方法，并针对非线性参数化不确定系统提出了基于参数识别的鲁棒输出跟踪器的设计方法。后者是本文为飞机防滑刹车系统设计输出跟踪器的理论基础，同时也是本文的创新点之一。在对结合力产生本质讨论的基础上，分析了滑水现象产生的原因和预防措施。

In order to make up the deficiency of ordinary trigonometric polynomial curves in aspect of shape adjustment, then in view of polynomial spline cannot represent some transcendental curves, a new kind of parametric trigonometric polynomial spline with a shape parameter is constructed by linear singular blending technique.

为了弥补普通三角多项式样条曲线在形状调整方面的不足，同时又考虑到多项式样条曲线不能精确表示一些超越曲线，我们利用奇异混合的思想构造了一种新的带有形状控制参数的三角多项式样条曲线。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。