Simply transform the point x and the point (x + n), subtract the two, and normalise. You now have the correct normal. It’s that simple. I used this method all t

Simply transform the point x and the point (x + n), subtract the two, and normalise. You now have the correct normal. It’s that simple. I used this method all the time while working on commercial game engines. You can use the same idea to invert transforms by simply imagining the transform as a 3D coordinate system in space and calculating the inverse relative to the origin and axis vectors of that coordinate system. No need to first generate the inverse transform matrix.