副法线的来由（binormal）

 Any given vertex has a tangent space as defined in Figure 12.4. The normal of the
vertex that you’re already familiar with points out from the triangle. The tangent and
the binormal, on the other hand, are new concepts. The tangent and the binormal
both lie on the plane of the triangle（这句话比较重要，切线和副法线都在三角形平面上）. The triangle is also UV mapped to the texture
(be it a diffuse map or a normal map). So what the tangent space actually describes
is a form of 3D texture space（切线空间其实一种3D纹理空间）（这里也可以说是一个模型内部零件的空间）.

 

Here’s some semi-useless knowledge for you. It is actually incorrect to talk
about binormals in this context. The mathematically correct term is actually
bitangent!（在数学中正确的叫法是副切线） ，However, people have been using the term binormal since no one knows
when（然而人们一直用副法线这种术语，因为没人知道当....这后面应该有话）. This is loosely because there can be only one normal per surface, but there can
be infinite amount of tangents on the surface（这里这么宽松是因为一个平面只有一条法线，而可以有无数条切线）.The term “bi” means two or “second
one,” which is why it is incorrect to be talking about a second normal in this case（"bi"表示两个或第二个）.
You can read more about this (and other interesting things) at Tom Forsyth’s
blog:
http://home.comcast.net/~tom_forsyth/blog.wiki.html

 

//下面是GPU精粹中在波中给出的三个线的数学来源，在公式里你可以有感性的认识

 

总而言之，副法线和切线都是平面的切线，这两条切线是对不同轴求导的结果，只是为了构成一个局部的切线空间而已。