There are two orientations in the project image that I drew. 

EASIER CONCEPT: The orientation on the top left reflects the projector image to the viewer.

HARDER (maybe impossible) CONCEPT: The projector image would be refracted through a lens (wish me luck finding this!) while the camera is behind the lens from the user’s perspective. The view of the user from the webcam would be distorted because of the lens, but this may be accounted for via software or with another lens (I’m probably assuming it’s easier to get a presentable image than it really is via either software or the lens).