How to distort a bitmap between the known points

I have four points and I need to draw a bitmap between these points. Points coordinates constantly change uniformly so the bitmap must be distorted so its vertices have the same coordinates as the points (see attached image).

I suppose that Papervision3D should be used.
Or maybe such implementation may be achieved with built in Matrix transformation?
I just need an assistance on what implementation should be used or where to look for such solution.
Thanks!