I can't understand

What I thought when I just hear about tangent space normals was this:

normal:::> is just the simple normal of the face

binormal":::> is the direction<<if i have 3 vertices positions(in world space) for a face>>: normalize(vertice2 - vertice1)

tangent:::>cross(normal, binormal)or the other way cross(binormal, normal)...i don't know

wouldn't this be much simpler?

so with this 3 vectors I just build a 3x3matrix multiply it by the normal of the texture and finally get the normals in world space

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this is my new question

I want to tranform this tangent normals of the texture to world space

I have three vectors in world space that represent a face of the object i am drawing

I just need a 3x3 matrix to rotate this tangent normals of the texture

the last vector of the matrix is the normal of the face: normalize(cross(v1-v0,v2-v0))

the middle vector will be what?

the first vector will be: cross(last vector,middle vector)