Irregular shape window to a different background world?

I have this light that shows a different view when shown on different things. It is working in that have objects phase in and out depending on the light. Now I want the background to show a different version where the light beam is drawn.

I tried having a RenderMaterial pull its colors from a camera and draw it to a polygon. It works for squares. I want to have a lopsided polygon instead of a simple square. Does anyone know how to accomplish this?