How to make a projection using a synthetic image given the camera's intrinsic and extrinsic parameters?

I've already got intrinsic and extrinsic parameters of a stereo system stored in a variable (calibration.mat). I've created the synthetic image model which I want to use to make a projection over the stereo system. How can I do this kind of projections? (Refer to the image attached for further explanation) I appreciate any help.