the plane that contains all the lines tangent to a specific point on a surface

some long range moving objects usually select local level coordinate as their navigation system , but short range objects may adopt inertial coordinate of tangent plane as their navigation systems.

远程运动对象常选地平坐标系为导航系，短航程的对象可选切平面惯性坐标系为导航系。

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。

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。

well,one way to think about it is in terms of tangent plane approximation.

我们可以从用切平面逼近的想法来入手。

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。

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。

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。

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。

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, in particular, this approximation is called the tangent plane approximation because it tells us, in fact, it amounts to identifying the graph of the function with its tangent plane.

这个近似办法称作,切平面近似，因为它告诉我们，可以通过切平面,来反映函数的图像。

and, here「s a tangent plane at the given point.

在这个给定的点有一个切平面。

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。

all satellite image are tangent plane projection obtained along the flight direction of satellite. in this paper.

卫星图像都是沿卫星飞行方向而获取的切平面投影图像。

ok, so now if you have a surface given by an evil equation, and a point on the surface, well, you know how to find the tangent plane to the surface at that point ok, any questions?

如果有一个由有点恶心的方程确定的曲面，以及在曲面上的一个点，你应该知道，如何找到这点处的切平面了,有问题么？

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。

this paper derives navigation error equations of tangent plane inertial coordinate.

本文推导了切平面惯性系统的导航误差方程；

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。

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。