tangent vector

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。

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The final finite-volume discretization equations are derived using the Hamilton principle. Meanwhile the global nodal force vector, mass matrix and tangent stiffness matrix of the cable are obtained.

再根据哈密顿原理导出了悬索大挠度振动的有限体积离散方程，推出了索的整体节点力向量、质量矩阵和切线刚度矩阵。

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All the discussion is based on two concepts of tangent hyperplane and normal vector.

整个算法建立在支撑超平面和法向量两个概念基础上。

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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。

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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。

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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。

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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。

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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。

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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。

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Many-Knot Curve Construction with Controlled Tangent Vector

带切向控制的多结点曲线造型方法

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Blending Rational Interpolation Curves with Given Tangent Vector

给定切失混合有理插值曲线

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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。

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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

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In particular, an easy case where you know you can get away without computing anything is, of course, if your vector field is tangent to the surface because then you know that there is no flux.

特别地，有一种简单的情况，是不用计算的，当向量场与曲面相切，没有通量。

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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。

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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。

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Meanwhile, the internal force vector and the element tangent stiffness matrix could be obtained from calculating directly the first derivative and second derivative of the element strain energy with respect to the nodal variables, respectively.

同时，采用矢量型转动变量，可以直接从计算单元应变能泛函对节点变量的一阶和二阶偏微分得到单元内力矢量和切线刚度矩阵。

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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。

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Hence, fairing a C~ 1 cubic spline curve with endpoint ( position and tangent vector) constraints will eventually lead to a cubic Hermite curve.

因此，光顺一条具有端点（位置和切矢）约束的C~1连续的三次样条曲线时，最终会得到一条三次Hermite曲线。

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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。

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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。

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A special kind of unabridged end conditions like wing is used in the interpolation of curves, it needs both radius of curvature and tangent vector perpendicular to chord line, and has been solved very successful by special processing.

其中一种比较特殊的完备边界条件是翼型条件，它要求在端点处有垂直于弦线的切线，并且具有给定的曲线半径；

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The unsteady state term was discretized using the full implicitly schemes. For the diffusion terms, the normal direction vector ( the first diffusion) and the tangent direction vector ( the second diffusion) were calculated by using the intersectant and iterative algorithm.

对于非稳态项采用全隐格式，对于扩散项，采用法向扩散项（一次扩散项）和切向扩散（二次扩散项）进行相互交叉迭代的算法。

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SVD Method for Selecting Tangent Vector in Tangent Distance

切线距离中选取切线向量的SVD方法

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After the template and point cloud are matched, point cloud is sliced by some planes to acquire sectional data. Every plane of these planes is constructed by one theoretical edge point and its corresponding tangent vector.

配准模板与点云数据，根据匹配后模板中每一离散点及对应的切矢信息构建平面，利用其对点云数据切片获得二维截面数据。

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