That means your normal vector points down.
那意味着法向量指向下。
That corresponds to normal vector pointing up.
那相当于法向量指向上。
The normal vector pointing up, here we know what it means.
法向量指向上，这里我们知道它是什么意思。
First of all, what does the normal vector to a cylinder look like?
先思考一下圆柱面的法向量？
The notation suggests it is a normal vector, so what does that mean?
从记号来看，是一个法向量，那它有什么意义呢？
K instead of using the vertical vector k, you use the normal vector I.
你用了法向量i，而不是竖直向量。
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。
So, for a sphere, the normal vector is divided by the radius of the sphere.
关于球体，法向量是,除以球的半径。
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。
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。
It's the dot product between the normal vector of a plane and the vector along the line.
这是平面法向量，和沿直线向量的点积。
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。
You can just multiply a normal vector by any constant, you will still get the normal vector.
一个法向量与任意常数相乘，还是法向量。
One thing that's on this picture that I haven't drawn down is the normal vector to the plane.
图上有个东东我没画,就是这个平面的法向量。
This value can be negative to extrude in the direction opposite the Face object's normal vector.
这个值可以为负，从而在Face对象的法向量的反方向上挤压。
Tasklets from the high-priority vector are serviced first, followed by those on the normal vector.
来自高优先级矢量的微线程先得到服务，随后是来自正常优先级矢量的微线程。
What if I give you a really complicated curve and then you have trouble finding the normal vector?
如果给你的是，一条很复杂的曲线，而又找不到法向量？
Then, if you had a flat disk with the curve going counterclockwise, the normal vector would go up.
就会得到一个被逆时针曲线包围的圆盘，法向量向上。
That is, it creates a 3-d figure by extruding in the direction of the Face object's normal vector.
也就是说，它在Face对象的法向量方向上进行挤压，创建一个3 - D图形。
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。
So, see, this coefficient becomes zero exactly when the line is perpendicular to the normal vector.
看到了吧，系数变为0了，当直线垂直于法向量的时候。
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。
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。
Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?
现在的问题是，曲面上这一小块儿的面积是什么，及其法向量是什么？
To find the surface element together with a normal vector, I would just take the cross-product between these guys.
为了找到带法向量的面元，我就取这两个的叉积。
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。
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。
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？
What we will do is just, at every point along the curve, the dot product between the vector field and the normal vector.
我们要做的是，沿着曲线的每一点上，取向量场和法向量的点积。
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。
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