It is really the tangent plane.
它确实就是切平面。
That is how we get the tangent plane.
这样我们就得到了切平面。
That's the equation of a tangent plane.
这就是切平面的方程。
That's one way to define the tangent plane.
这是定义切平面的方法。
We are replacing the graph by its tangent plane.
我们用函数的切平面来替代它的图像。
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。
Let's think about the tangent plane with regard to a function f.
我们来考虑，关于函数f的一个切平面。
If we were moving on the tangent plane, this would be an actual equality.
如果我们在切平面上移动，这将会是一个真正的等式。
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。
Being perpendicular to the surface means that you are perpendicular to its tangent plane.
垂直于曲面也意味着垂直于它的切平面，垂直于曲面也意味着垂直于它的切平面。
All satellite image are tangent plane projection obtained along the flight direction of satellite.
卫星图像都是沿卫星飞行方向而获取的切平面投影图像。
And, at this point, I have the tangent plane to the level surface OK, so this is tangent plane to the level.
在这点上，我们有一个切于等值面的切面，这就是等值面的切平面。
Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point.
那意味着，梯度向量在这点上，垂直于切平面或者是等值面。
Say you have a minimum, well, the tangent plane at this point, at the bottom of the graph is going to be horizontal.
如果你说这是个极小值，那么这点的切平面应该是水平的。
And so, in particular, if we set this equal to zero instead of approximately zero, it means we'll actually be moving on the tangent plane to the level set.
而且，特别地，如果我们令此函数为零，而不是近似为零，它意味着我们在水平集的切平面上移动。
Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface. Let's try to see how that works.
现在，假设曲面上有两条相交切线，那么这两条切线可以确定一个切平面，我们来看看这个平面是怎么搞出来的。
The object 's surface often possesses some particular geometric continuities such as the continuity of position, of the tangent plane and even of curvature.
实体的表面一般都具有一定的光滑性，比如位置连续、切平面连续甚至曲率连续。
See the point in the middle, at the origin, is a saddle point. If you look at the tangent plane to this graph, you will see that it is actually horizontal at the origin.
我们来看中间的那个点，在原点上，那就是一个鞍点，在这点做一个切平面,你可以看到这个切平面,是在原点上水平的。
We deduce the eigenvalues of 2-neighbors subdivision matrix of the scheme, and prove that the subdivision surface is convergent, and has property of tangent plane continuity.
通过对细分矩阵特征值的理论分析，证明了文中方法的细分极限曲面收敛且切平面连续。
That's actually pretty neat because there is a nice application of this which is to try to figure out, now we know, actually how to find the tangent plane to anything, pretty much.
这个性质很漂亮，因为它有一个很好的应用，可以用来，求算很多东西的切面。
For the tangent plane can be achieved by running continuous power flow method only once, it's possible to realize the online calculation of the static voltage stability region.
由于利用文中方法只需通过一次连续性潮流计算即可获得稳定域边界上的切平面，使得稳定域的在线计算及可视化成为可能。
We know that f sub x and f sub y are the slopes of two tangent lines to this plane, two tangent lines to the graph.
我们知道fx和fy是,曲面上两条切线的斜率。
The plane that contains all the lines tangent to a specific point on a surface.
包含所有在表面上的一个特殊的点相切的线的平面。
The problem of attaining the tangent equation of a certain point on a quadratic curve is basically solved in plane analytical geometry.
平面解析几何对“求过二次曲线外的点所引曲线切线的方程”的问题，未给出一般的方法和公式。
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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