I am a little bit confused in terms of what this slide is trying to explain. I understand that we want to project the original chessboard picture to a seemingly tilted surface so that we can reach the "correct" pic from the original. However, I don't understand how the "affine" one works and why we can split the quadrilateral like this. As I see from the affine picture, it seems like we are splitting the quadrilateral in another direction.