 Ok, hello everyone welcome back ah continuing onward um today we are going to change topics of fair amount. Let me just remind you a little bit of what we have done so far. So, so far I have given you a high level birds eye view in the first lectures that covered the software hardware and human sensation and perception parts and then I spent time going over um geometric models and transformations that are applied to them and then went through the entire chain of transformations so that you can go from defining movable objects in the world or movable bodies in the world and stationary ones put them all together and then determine through a chain of these transformations where your points in your original models where you place them are going to end up on the screen. So, it will end up with pixel coordinates at the end um there were several parts to that and um not going to cover them all in detail again here, but I just wanted to remind you of that and so we had the rigid body transformation, the eye transformation, the canonical view transformation and the viewport transformation and um there is going to be a distortion transformation that is applied at the end to cover optical distortions which is something we are going to talk about today. And um also in these matrices the canonical view transform broke down into a scaling and translation matrix and a perspective transformation matrix and as one of the students pointed out at the end of class yesterday um the scale and translation matrix is a little bit too general for our purposes. So, we can simplify it a bit because by the way I said everything up in class last time the viewing frustum is perfectly centered and so because of that symmetry um this component goes to 0 and this component goes to 0 because r plus l is 0 and t plus b is 0. However, the near and far planes are not perfectly centered so that the origin is is directly between them um so this term stays. So, if you want to simplify that matrix from last time this is how to do that.