That corresponds to normal vector pointing up.
那相当于法向量指向上。
Let's break the name down. The "normal" is a vector perpendicular to a surface, which we can use to calculate lighting.
首先我们从名字上开始分析，所谓“法线”指的是垂直于平面的向量，我们使用这个来计算光照。
That one would be pointing kind of to the back slightly up maybe, so like that. And now your middle finger is going to point in the direction of the normal vector.
曲面的方向有点向后向上,应该差不多像这样，那么现在你的中指,指的方向就是法向量的方向了。
Well, to get our conventions straight, we should take the normal vector pointing up for compatibility with our choice.
为了配合约定习俗,选择相容的、指向上的法向量。
Ok, if we look at it near here, if we walk along this way, the surface is to our right.so, we should actually be flipping things upside down. The normal vector should be going down.
我们看看这里，如果我们沿着这条路走，曲面就在我们的右边，我们应该是把它颠倒一下，这个法向量也应该向下。
Let me show you a picture. The rule is if I walk along C with S to my left then the normal vector is pointing up for me.
给你们看张图片，“相容”就是,如果我沿着C走，而且S在左边，法向量就是朝上的。
And let's say I want to Orient my cylinder so that the normal vector sticks out.
我给这个圆柱确定了方向，即法向量指向圆柱之外。
And to find the height of this thing, I need to know what actually the normal component of this vector is.
为了求出高度，需要知道这向量的垂直分量是多少。
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 fact, if you try to follow your normal vector that's pointing up, it's pointing up, up, up.
事实上，如果你随着你的法向量，一直朝上走。
There's no way to choose consistently a normal vector for the Mobius strip So, that's what we call a non-orientable surface.
为Mobius带选一个始终如一的的法向量是不可能的,这就是所谓的不可定向的曲面。
That is our convention to get a unit normal vector that points to the right of the curve as we move along the curve.
这是约定的得到单位法向量的方法，这种做法使得，当沿着曲线行进时，法向量始终指向右手方向。
When we know two vectors in a plane, it let us find the normal vector to the plane, and that is what we need to find the equation.
当我们已知平面上的两个向量，我们就可以找到，这个平面的法向量，然后我们就可以用法向量来找到方程。
In fact, our vector field and our normal vector are parallel to each other.
事实上，给定的向量场与法向量是相互平行的。
It is this guy.If you continue to follow your normal vector, see, they are actually pointing up and into the paraboloid.
就是这它了，如果你继续跟着法向量看，会看到它们实际上，指向上并且指向抛物面里。
OK, the best way to it, now that we have the gradient vector, is actually to directly say oh, we know the normal vector to this plane.
最好的方法是，既然我们已经有了梯度向量，就可以直接说,我们知道了切平面的法向量。
But the usually traditional settings would be to take your normal vector pointing maybe out of the solid region because then you will be looking at flux that is coming out of that region of space.
但通常的习惯是,把立体区域上的外法向量规定为其定向,因为这么做之后，当你观察通量时会发现,它是从区域内部向外流动的。
Hopefully, you can see that if I take a normal vector to the sphere it is actually pointing radially out away from the origin.
我希望大家能够了解，如果我将法向量平移至球面，那么它将以原点为心向外放射。
Just to reiterate what I said, positively here means, because we are going counterclockwise, the normal vector points out of the region.
再说一遍，这里“正的”意味着…，由于是逆时针走向，法向量指向区域外侧的。
Another way to do it, of course, would provide actually parametric equations of these lines, get vectors along them and then take the cross-product to get the normal vector to the plane.
当然也有另一种方法，就是用参数方程表示这两条直线，用两条直线的方向向量作外积，从而得到切平面的法向量。
This is a normal vector of the same length as n, well, up to sign.
这是与N长度相同的法向量，只是符号不定。
And, we know how to find a normal vector to this plane just by looking at the coefficients.
我们已经知道，如何根据系数找到这个平面的法向量。
It can be a normal vector of any length you want to the surfaces.
它可以是曲面上想要的任意长度的法向量。
You can remember, if it helps you, that if a surface is to your right then the normal vector will go down.
你也可以这样记，如果曲面在你的右边,那么法向量就向下。
And we looked at the component of a vector field in the direction that was normal to the curve.
我们研究的是，向量场在曲线法向量方向的情况。
And, if you pay attention to the orientation conventions, you'll see that you need to take it with normal vector pointing up.
如果你注意到了方向的约定，你会发现它的法向量是向上的。
The orientation that will work for this theorem is choosing the normal vector to point outwards.
对于这个定理，我选择的方向是,指向外的正方向。
And we know how to find a normal vector to the level set, namely the gradient vector is always perpendicular to the level set.
我们是知道如何去求水平集的法向量的，也就是垂直于水平集的法向量。
Now, if you wanted the unit normal vector to compute flux, then you would just scale this guy down to unit length, OK?
如果想用单位法向量来计算通量，还得先把它标准化到单位长度？
If you imagine that you have this big cylindrical type in front of you, hopefully you can see that a normal vector is going to always be horizontal.
想象一下，你的面前有一个大圆柱，希望大家可以想象到，其法向量总是水平的。
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