There are three methods for tangent vector discussed in this paper.
本文指出了切线向量的三种求法。
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。
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。
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。
Then, if I choose any vector in that tangent plane.
那么如果我选择了任何位于切平面的向量。
We know that the gradient is perpendicular to this vector that's tangent to the level surface What about other vectors tangent to the level surface?
我们知道梯度向量垂直于这个向量，而速度向量是相切于等值面的，其他相切于等值面的向量，又如何呢？
It has a hat because it's a unit vector, and t because it's tangent.
这上面有一个帽子表示它是单位矢量，T表示它是切线。
OK, and that's going to be the normal vector to the surface or to the tangent plane.
这就是切平面的，或者说这个曲面的法向量。
And, in some cases, for example, if you know that the vector field is tangent to the curve or if a dot product is constant or things like that then that might actually give you a very easy answer.
例如，在某些情况下，如果已知向量场与曲线相切，或者内积是一个常数等等，那么结果将会很简单。
That is how we reformulated it. That means we take our curve and we figure out at each point how big the tangent component I guess I should probably take the same vector field as before.
这是另一种形式，它意味着,要求出每点处向量在切向量方向的分量,我还是用之前那个向量场吧。
So, the velocity vector is going to be always tangent to the curve.
速度向量总是与曲线相切的。
If you remember what we did several times, well, along the circle that vector field now is tangent to the circle.
我们做过若干次了，沿着圆，向量场与圆相切。
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。
The original texture coordinate and height values are already represented in tangent space, so the eye vector must be as well.
原始的材质贴图坐标和高度数据已经在切线空间中了，因此视向量最好也能如此。
The eye vector can be created in global coordinates by subtracting a surface position from the eye position and transforming the resulting vector into tangent space.
视向量能够在全局坐标系中通过视点坐标减去表面坐标来创建，并且要把结果转换到切线空间中。
That is a vector field in which the trajectories are going to be circles centered in the z-axis and our vector field is just going to be tangent to each of these circles.
这是一个向量场，其中旋转轨道是，以z轴为圆心的圆周，并且这个向量场与每个圆相切。
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。
Then, based on the CR formulation, the internal force vector and tangent stiffness matrix of large rotation and small strain space bar and plane beam element are deduced.
其次，基于CR列式法推导出了大旋转小应变空间杆单元及平面梁单元的内力矢量及切线刚度矩阵；
Then, based on the CR formulation, the internal force vector and tangent stiffness matrix of large rotation and small strain space bar and plane beam element are deduced.
其次，基于CR列式法推导出了大旋转小应变空间杆单元及平面梁单元的内力矢量及切线刚度矩阵；
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