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• The normal vector pointing up, here we know what it means.

向量指向这里我们知道是什么意思

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• 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条路走曲面就在我们右边我们应该它颠倒一下，这个向量应该向下

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• You will get some sort of mesh grid on your surface and you will look at a little parallelogram that is an elementary piece of that mesh and figure out what is its area and normal vector.

曲面上做一些网格看到一个网上的每一小块儿，都平行四边形，我们要弄清楚面积向量什么

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• And that is, in general, not a unit normal vector.

通常不是一个单位向量

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• 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法向量

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• And we know how to find a normal vector to the level set, namely the gradient vector is always perpendicular to the level set.

我们知道如何水平向量的，也就是垂直水平向量

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• Tasklets from the high-priority vector are serviced first, followed by those on the normal vector.

来自高优先矢量的微线程先得到服务随后是来自正常优先矢量的微线程。

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• This is a normal vector of the same length as n, well, up to sign.

N长度相同法向量只是符号不定。

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• Now, let's multiply that by the unit normal vector.

现在单位向量乘以那个

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• Now, if you wanted the unit normal vector to compute flux, then you would just scale this guy down to unit length, OK?

如果单位向量计算通量，还得先标准化单位长度

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• And, if you pay attention to the orientation conventions, you'll see that you need to take it with normal vector pointing up.

如果注意到了方向约定发现法向量向上的。

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• That means your normal vector points down.

意味着向量指向

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• It's the dot product between the normal vector of a plane and the vector along the line.

平面向量沿直线向量

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• Namely, we will be saying the /a normal vector is x, y, z over a, plus or minus depending on whether we want it pointing in or out.

我们容易知道,法向量为，正负取决于指向外面还是里面。

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• One thing that's on this picture that I haven't drawn down is the normal vector to the plane.

有个东东,就是这个平面向量

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• 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.

当然另一种方法，就是用参数方程表示两条直线，用两条直线方向向量作外从而得到平面向量

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• You can remember, if it helps you, that if a surface is to your right then the normal vector will go down.

也可以这样如果曲面右边,那么向量向下

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• And, in fact, if you try to follow your normal vector that's pointing up, it's pointing up, up, up.

事实上如果随着向量，一直上走。

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• The normal vector will just be the gradient.

向量就是梯度向量

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• So, for a sphere, the normal vector is divided by the radius of the sphere.

关于球体向量,除以半径

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• That is, it creates a 3-d figure by extruding in the direction of the Face object's normal vector.

就是说Face对象向量方向进行挤压创建一个3 - D图形

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• And so the normal vector is going towardS what is up for me.

所以向量指向的上方。

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• That corresponds to normal vector pointing up.

相当于向量指向

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• 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.

我们已知平面上的两个向量我们就可以找到这个平面向量然后我们就可以用法向量找到方程

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• Why else would you know a normal vector?

还有什么原因知道向量

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• In fact, our vector field and our normal vector are parallel to each other.

事实上，给定的向量向量相互平行的。

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• 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.

通常习惯,立体区域向量规定为其定向,因为这么做之后，当观察通量时会发现,它是从区域内部向外流动

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• Why would we ever know a normal vector?

为什么我们知道向量

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• The notation suggests it is a normal vector, so what does that mean?

记号来看，一个向量它有什么意义呢？

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• If you have a plane, ax+by+cz=d then the normal vector would just be .

如果一个平面，，，ax+by+cz=d那么向量就是

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