This paper goes into very detail about the principal reference system, which is introduced as their geometric coordinate, and the relationship of the surface parameters with the coordinate. They solved the surface parameters point by point instead of using a global estimated function. This is a very good approximation to get the real surface, since if we get more reconstructed points, we could have more information to formulate the actual surface. The problem here is that this method only works on specular surfaces. When the surfaces are not ideally reflective or the angle of reflection is distorted, the surface would not be correctly reconstructed. I'm just thinking of that can this method reconstruct the surface of a distorting mirror.