基于对生物复眼几何结构的模拟，提出一类新颖而有效的数据处理方法——方向量子化方法。
A new data representation method called direction quantization representation is presented by simulating a simplified geometric model of biological compound eye.
梯度向量的垂直方向，为什么是这样而不是另外一个方向？
Does the gradient vector, why is the gradient vector perpendicular in one direction rather than the other?
方向基本和这里的单位切向量一致。
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。
That is our convention to get a unit normal vector that points to the right of the curve as we move along the curve.
也就是，如果我给你一个单位向量，试问，我沿着这个方向移动，我的函数值会变化得多快呢？
OK, so if I give you a unit vector, you can ask yourself, if I move in the direction, how quickly will my function change?
梯度向量方向是,在给定点处指向函数增加得最快的方向。
The gradient is the direction in which the function increases the most quickly at that point.
也就是说，如果朝该方向运动，函数值变动得最剧烈，那么相应的斜率就是梯度向量的模长。
OK, so if I go in that direction, which gives me the fastest increase, then the corresponding slope will be the length of the gradient.
从而法向量的方向是竖直向上或向下的。
The normal vector is just sticking straight up or straight down.
这里我们并没有曲面定向的概念，能做的就是，从两个法向量中选出一个作为正方向。
Here we don't have a notion of orienting the surface other than by precisely choosing one of the two possible normal vectors.
因此，优化解决方案是从轴的原点沿 (1,-1)方向作为方向向量指向多面体边界的最远点。
Therefore, the optimal solution is the farthest point on the polyhedron boundary from the axis' origin using the direction (1,-1) as a direction vector.
只有向量方向，即分振幅之间的比值，是重要的。
Only the direction of the vector, the ratios between the component amplitudes, is important.
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。
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.
总的来说，您需要一个与照射平面相垂直的方向向量。
The general idea is that you need a direction vector that is orthogonal to the lit surface.
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。
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.
法向量方向上，分量为零。
如果取一个有旋的向量场，流体流动方向是环绕某个坐标轴的，那么就会发现它的散度是零。
And, if you take a vector field where maybe everything is rotating, a flow that's just rotating about some axis, then you'll find that its divergence is zero.
我所做的就是把F投影到切向量方向上，得出F沿着曲线的值,然后再把这些加起来。
What I do at any point is project F to the tangent direction, I figure out how much F is going along my curve and then I sum these things together.
我给这个圆柱确定了方向，即法向量指向圆柱之外。
And let's say I want to Orient my cylinder so that the normal vector sticks out.
我们研究的是，向量场在曲线法向量方向的情况。
And we looked at the component of a vector field in the direction that was normal to the curve.
这是另一种形式，它意味着,要求出每点处向量在切向量方向的分量,我还是用之前那个向量场吧。
That is how we reformulated it. That means we take our curve and we figure out at each point how big the tangent component I guess I should probably take the same vector field as before.
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。
And, if you pay attention to the orientation conventions, you'll see that you need to take it with normal vector pointing up.
那么在我画的这幅图中,充满了方向指向原点的向量场,离原点越远，它就越小。
The picture, if I really wanted to draw a picture, would be everywhere it is a field that points towards the origin. And if I am further away then it gets smaller.
即竖直方向的单位向量。
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。
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.
用沿着向量方向的平面,切开图像,然后看图像的剖面图，找出斜率。
We'll be slicing things by a plane that is now in the direction of this vector,u and we'll be looking at the slope of the slice of the graph.
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。
And, if I look carefully at the orientation convention, Stokes I have to take the normal vector pointing up again.
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。
That is, it creates a 3-d figure by extruding in the direction of 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。
This value can be negative to extrude in the direction opposite the Face object's normal vector.
现在我实际上想知道的是，这两个向量是什么，我们称它们为，U和，两者对应的是x方向和y方向一点位移？
Now what I want to find,actually, V is what are these two vectors, let's call them U and V, that correspond to moving a bit in the x direction or in the y direction?
其中一种说明了，在向量场上，沿逆时针方向，向量做的功等于，平面区域上旋度F的二重积分。
So, one of them says the line integral for the work done by a vector field along a closed curve counterclockwise is equal to the double integral of a curl of a field over the enclosed region.
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