Test for the math needed to transform a position given 4 rectangle points. I might be doing the math incorrectly, idk. Made it all by myself in a few minutes. Move your mouse (the black point, normally should be in the purple square) to affect the red point (normally should be in the green square). Use the sliders to move the green square's points. Press H to show or hide the extra interface.
v1.1: updated transform math a bit