Distort camera viewport with world space coordinates

Hi guys!

I have this free moving camera and geometry with a hole. (For sketching purposed I use a plane) This hole (everything I see through the hole) needs to always fill the camera viewport fullscreen.

I don't want to distort geometry, I need to distort the projection matrix of the camera itself. I can calculate the screenspace points of the "plane's" four corners. Does anybody know how to proceed?