Well, that means the gradient is actually perpendicular to the tangent plane or to the surface at this point.
那意味着，梯度向量在这点上，垂直于切平面或者是等值面。
Now, if I have two lines tangent to the surface, well, then together they determine for me the tangent plane to the surface. Let's try to see how that works.
现在，假设曲面上有两条相交切线，那么这两条切线可以确定一个切平面，我们来看看这个平面是怎么搞出来的。
And, at this point, I have the tangent plane to the level surface OK, so this is tangent plane to the level.
在这点上，我们有一个切于等值面的切面，这就是等值面的切平面。
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。
Being perpendicular to the surface means that you are perpendicular to its tangent plane.
垂直于曲面也意味着垂直于它的切平面，垂直于曲面也意味着垂直于它的切平面。
The plane that contains all the lines tangent to a specific point on a surface.
包含所有在表面上的一个特殊的点相切的线的平面。
The object 's surface often possesses some particular geometric continuities such as the continuity of position, of the tangent plane and even of curvature.
实体的表面一般都具有一定的光滑性，比如位置连续、切平面连续甚至曲率连续。
We deduce the eigenvalues of 2-neighbors subdivision matrix of the scheme, and prove that the subdivision surface is convergent, and has property of tangent plane continuity.
通过对细分矩阵特征值的理论分析，证明了文中方法的细分极限曲面收敛且切平面连续。
We deduce the eigenvalues of 2-neighbors subdivision matrix of the scheme, and prove that the subdivision surface is convergent, and has property of tangent plane continuity.
通过对细分矩阵特征值的理论分析，证明了文中方法的细分极限曲面收敛且切平面连续。
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