When I was working on Mathsurf, I realized that the mapping function could apply to other mesh as well as a simple rectangular grid. Same method as we utilize in some differential geometry. We override the domain of a regular grid to non perpendicular domains. Now we can use other geometry as a source of the initial domain. Basically the operation of Mathdeform is very similar to modifiers likes twist or bend in 3ds max. They don’t change the topology of the object, they just change the position of vertices in an editable mesh or poly objects (or any kind of 3ds max object that can produce a regular mesh on demand).the difference is Mathdeform pick the object in the scene and create new object separately likes the compound objects but modifiers affect the object in place.

Now in combiniation of Mathdeform and other kind of geometries as well as Mathsurf & Mathcurve you would be able to create complex topological geometries that never can do before.