Parameterization of generated surface wrt deform modifiers


can I somehow get the mapping (transformation matrix) between a deform modifier and the generated surface in Blender?
I assume this is very generic, so an alternative would be to get the deformation of the generated surface, every time I move around a deform modifier (e.g. a lattice point), let’s say by a small displacement vector A. Is this possible?
The only way I can imagine to get the deformation vector of the surface is by exporting the two surfaces (the original one and the one generated by a lattice movement) in stl format or similar and then “subtract” the two stl files, assuming they are consistent.

Thanks in advance,