Mesh boolean operations

I’m looking for some tips on subtracting one mesh from another, for my specific use I have a deformed plane and a (probably convex) object. I want to use the object to cut a hole in the deformed plane:

I know it might be a bit more complex then it looks like but if anyone know of a (working) python library that can make it simpler, or any online papers about the topic, then I’d much welcome a link.

If you are only wanting to do it in python, I have no idea. But several modeling programs have the capability. 3d studio max and certain versions of Wings3d are the ones that I have experience with.