By now you realize that surface normals are the most important geometric surface characteristic used in computing illumination models. They are used in computing both the diffuse and specular components of reflection.

However, the vertices of a model do not transform in the same way that surface normals do. A naive implementer might consider transforming normals by treating them as points offset a unit length from the surface. But even this approach will not work. Consider the following two dimensional example.

The problem with transforming normals occurs when objects undergo an anisotropic scaling (scaling that is not uniform in all directions). Such scaling results only from affine modeling transforms (Why not Euclidean transforms?).