This dissertation presents a definition of general offset curve which has fixed offset distance but variable offset direction . The offset direction is defined by the local coordinate system which is formed of the tangent vector and the normal vector of every point on the curve .

本文利用曲线上各点的 切 向量和法向量所形成的局部坐标系来确定等距方向，从而给出一种广义偏距曲线的新定义。

The mathematical representations of space curve in mathematics have many forms and the means by which to get the tangent vector varies according to the various representations .

空间曲线的数学表示形式有多种，而不同的表示形式，求其 切线 向量的方法也不同。

There are some mathematical representations of space curves which will probably be met in actual engineering and this article discusses how to get the tangent vector of these space curves according to their various mathematical representations .

本文就工程实际中可能出现的几种空间曲线的数学表示形式，分析其 切线 向量的求法。

The method of mapping through tangent vector is introduced to obtain ideal point location in physical space which improves the mesh quality around the poles .

采用 切 矢映射法，使得理想点的求取可以在物理空间中实现，提高了周期性退化曲面极点处网格的质量。

In this paper the tangent vector loading method and the boundary element restrain method was presented .

采用了 切线 矢量加载和边界单元的约束方法建立分析模型。

The purely kinematical equation for the tangent vector of a line element is derived .

导出了线元 切 向量的变形方程以及拉伸轴在极射赤面投影图上位置变化计算公式。

New Geometrical Explanation of the Definition of Tangent Vector on Differential Manifolds

微分流形上 切 向量定义的新几何解释

According to the calculation theory the tangent vector the velocity and the normal vector on a given point of the circle of tool nose are coplanar .

根据此原理，摇盘回转时，刀尖圆上给定点的 切线 向量、绕摇盘回转的速度方向和法矢这三个向量共面。

We discuss three important aspects : preprocessing of gait image feature extraction and classification . We emphasis on silhouette segmentation algorithm and silhouette description using Tangent Vector Descriptor .

本文论述了构成步态识别系统的步态图像预处理、特征提取、训练识别三个方面内容，重点讨论了图像预处理轮廓分割算法和以 切 向量描述的轮廓特征提取技术。

The tangent vector at every data point is identified through the localized quadratic spline function at first . The tangent vectors and data points approximately determine the shape of the four spline curve .

首先用二次样条函数方法局部化地在每个数据点处确定一个 切 矢量，数据点和切矢量大致决定了四次样条曲线的形状。

Many-Knot Curve Construction with Controlled Tangent Vector

带 切 向控制的多结点曲线造型方法

This paper discusses correspondence between homogeneous polynomial vector field of even degree Q ( x ) in R3 and the induced tangent vector field QT ( x ) of Q ( x ) on S2 and some geometric properties of solutions . The nonexistence of limit cycles is proved .

本文讨论了偶次多项式齐次向量场和S2上的导出 切 向量场之间的对应关系和轨迹的一些几何性质，并证明了Q（X）不存在极限环。

The chapter V researches the isoperimetric problem for Bezier curves with tangent vector constraint which is to add a constraint on the basis of chapter IV and solve the problem using Lagrange multiplier method .

第五章研究了带 切 矢约束条件的Bezier曲线中的等周问题，是在第四章实现的等周问题的基础上，多加了一个约束条件，并用拉格朗日乘数法解决这个问题。

In this paper we study a norm denned on tangent vectors to earthquake curves . We show first that the norm of the initial tangent vector to an earthquake curve ht is equivalent to the Thurston norm of the earthquake measure a which determines the curve .

本文研究了定义在earthquake曲线切向量上的范数，首先证明了一条earthquake曲线ht上初始 切 向量的范数等价于earthquake测度σ的Thurston范数。

SVD Method for Selecting Tangent Vector in Tangent Distance

切线距离中选取 切线 向量的SVD方法

Then actually there are ways you can use basically differentials and constrained partials to figure out what the tangent vector to the curve is and so on .

然后，可以用微分关系，或受约束的偏微分来表示，曲线的 切 向量，就是这样了。