The Normal Map node provides the normal of an object in global space. I also need the tangent or bitangent (either's fine because a cross product will produce the third). This is a problem because the only ways I can see to get them - the Geometry node's Tangent output, or the Tangent node - only provide the tangents without any way to apply the normal map first.
I've tried to create a "bitangent map" node to basically fool the Normal Map node, under the logic that by manipulating the channels of the normal map, I can make the normal point towards the bitangent instead. It swaps G and B, and inverts R so the handedness is maintained.
But I'm not getting the expected result, so I'm wondering if my logic is flawed or not.