Yeah, I think I’d have to update the tangent computation for my node setup to work. Normal cross product with coordinate minus center should work.
Edit: I just realized that the situation is more complicated: the anisotropic calculations requires normal vectors in global/object space, but if the texture is evaluated in UV coordinates, the connection to global coordinates is lost…
Edit 2: I think using the Tangent node set to UV makes it possible to compute a correct tangent in global coordinates. The output of the Subtract node in the lower left is the vector pointing from the perlage center to the surface point in UV coordinates I took the output of the tangent node to be one basis vector, the normal vector to be the second and computed the third basis vector with the cross product. I interpreted the UV coordinates to be the first and third coordinates in this coordinate system (the coordinate related to the normal direction being zero). I have no idea whether this is correct, but it works for anisotropy: