How much of screen transform is, in implementation, cached? I imagine that for especially limited variations with large render time, it might be useful, but am not sure exactly if/how it would be done?

I'm definitely missing something here. In the top-middle image, the camera should be looking at the side view of the cube person. But why do we see the front view after it's mapped to 2D?

@azul I think this diagram is meant to be more of a conceptual representation than a literal one. Since we're looking at 2D representations of 3D space and a 3D cube person and we only have the one 2D image of the cube person, we're limited in the angles of the cube person we can literally see in the diagram. The top-middle image looks like the camera is viewing the person side-on, but it's really meant to represent the camera looking at the cube person head-on.