图上有个东东我没画,就是这个平面的法向量。
One thing that's on this picture that I haven't drawn down is the normal vector to the plane.
重点：直线的方向向量与平面的法向量的应用。
Key points: application of the direction vector of a line and the normal vector of a plane.
我们已经知道，如何根据系数找到这个平面的法向量。
And, we know how to find a normal vector to this plane just by looking at the coefficients.
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。
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.
除了让人来分辨这个模型的正误外，还有另外一种方法判断平面的法向量是否朝向外面。
Short of getting a human involved to look at the model, there are ways to check that the normals are pointing outwards.
求切平面方程的一般方法是先求切平面的法向量(借助偏导)，再用点法式写出切平面的方程。
The common method to quadric surface equation is to get the Normal Component first, and then write out the equation through dot method.
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。
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.
这就是切平面的，或者说这个曲面的法向量。
OK, and that's going to be the normal vector to the surface or to the tangent plane.
图像梯度修正是将图像梯度方向旋转到尽量与法向量在图像平面的投影反向一致的方向上。
The revision of the image gradient is to revolve it to the reverse direction of the normal vector's projection on the image plane.
图像梯度修正是将图像梯度方向旋转到尽量与法向量在图像平面的投影反向一致的方向上。
The revision of the image gradient is to revolve it to the reverse direction of the normal vector's projection on the image plane.
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