Whenever vertices are transformed, normal vectors should also be transformed so that they point in the right direction. We could consider using the Model-View matrix that transforms vertices to do this, but this approach is problematic: the Model-View matrix will not always keep the perpendicularity of normals, as illustrated by the following diagram:
This problem occurs if there is a unidirectional (one axis) scaling transformation or a shearing transformation in the Model-View matrix. In our example, we have a triangle that has undergone a scaling transformation on the y-axis. As you can see, the N' normal is no longer perpendicular after this kind of transformation. How do we solve this?
