In Ghost Land we had a problem that the projector/beamer was projecting the image as a quadrilateral. So we needed a translation from quadrilateral back to a rectangle (without that if you would hit the projected top-right corner, it would be translated as shifted to left). With Andrew’s we got a working solution.
In case that you need to translate a point from one quadrilateral to another (for example to a rectangle) in Java or Processing - you can use the source from 9-volt/quadrilateral_translation.
Here is an example of points translation: