在曲面上做一些网格，你会看到一个网上的每一小块儿，都是小的平行四边形，我们要弄清楚它的面积和法向量是什么。
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.
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？
Well, the question we have now is what is the area of this little piece of surface and what is its normal vector?
平面上有一个三角形,用两个向量描述,记作A、B，怎样求三角形的面积？
Let's start with a triangle in the plane Well, then we need two vectors to describe it say A and B here. How do we find the area of a triangle?
这把一个向量场的线积分，和另外一个向量场的曲面积分联系起来。
This relates a line integral for one field to a surface integral from another field.
这面积，约等于平行四边形的一半，我能用向量表示它。
So, the area is approximately equal to one half of the area of a parallelogram that I could form from these vectors.
这个曲面积分，不是同一个向量场。
OK, and that surface integral, well, it's not for the same vector field.
向量dS与曲面垂直,并且它的长度与面积元素有关。
Vector dS is a vector which points perpendicular to the surface and whose length corresponds to the surface element.
此外，本文还论述了向量的其它应用如：求面积、体积及证明共线与在共面问题。
In addition, this article also elaborated the vector other applications for example: asks the area, the volume, and the proof altogether line and in identical plane for the question.
优化特征选择，选定面积、周长、长轴、短轴、欧拉数、几何矩等共12个特征参数作为神经网络输入向量进行分类试验。
Optimization of feature selection, we select area, perimeter, long axis, short axis, Euler number, geometric moments, and a total of 12 feature parameters as input vector.
由于分类的依据是气泡表面积的大小，确定了圆面积和圆形度两个最能表征类圆形表面积的分量组成分类特征向量。
Area and circularity act as two elements of the eigenvector for they can remarkably characterize the surface area of the bubbles.
由于分类的依据是气泡表面积的大小，确定了圆面积和圆形度两个最能表征类圆形表面积的分量组成分类特征向量。
Area and circularity act as two elements of the eigenvector for they can remarkably characterize the surface area of the bubbles.
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