Virtual production with a vive controller and projector

Hi guys,
I’m wanting to set up a virtual production setup

I have a projector in the room.It projects onto the wall.

I’ve got a vive controller connected to a physical camera in the real world.

Now i want to project onto the wall a UE4 camera view so that when i shoot it with my practical camera it looks as if the wall is being extended into a virtual set.

Any idea on this setup?