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？
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。
If you have a plane, ax+by+cz=d then the normal vector would just be .
如果你有一个平面，，，ax+by+cz=d，那么法向量就是。
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。
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 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。
Calculates the normal vector projecting from the hand relative to the controller.
计算手掌相对于控制器的法线向量。
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。
Key points: application of the direction vector of a line and the normal vector of a plane.
重点：直线的方向向量与平面的法向量的应用。
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。
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。
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。
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。
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。
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, 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。
And, if I look carefully at the orientation convention, Stokes I have to take the normal vector pointing up again.
如果我仔细考虑了方向的约定，定理告诉我们，Stokes, theorem, tells, me, that，法向量必须再次指向上。
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。
And a new method to estimate the normal vector of the surface in Direct Voltime Rendering in Image Space is introduced.
在象空间中的直接体绘制方法中，本文提出了一种新的估计表面法向量的方法。
According to the characteristic of the wave field data, a simple algorithm is used to calculate the normal vector at the nodes.
文中针对表示波浪面的数据集的特性，采用了一种简单的节点法矢量算法。
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。
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。
But, when it comes to looking for the normal vector, be rest assured that the normal vector to a horizontal plane is just vertical.
但是在寻找法向量时，可以确定法向量与水平面垂直。
Nor: Uses the direction of the normal vector as coordinates. This is very useful when creating certain special effects (see below).
法向：使用法向量的方向作为坐标。这在创建某些特效时非常有用（见下文）。
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。
Well, the normal vector is either coming straight at us, or it's maybe going back away from us depending on which orientation we've chosen.
法向量或者指向我们，或者背向我们,这要根据我们选的方向来定。
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