I envision a modifier that “bends space” within a certain region. In the upper part of the attached image, X space stretches in the -X direction. Below that, XYZ space shrinks in the -X direction, yielding a “forced perspective” effect.
I wrote up a 2D example for you (EDIT: this behavior corresponds to the top half of the original image): This should clarify things I hope!
Writing a modifier shouldn’t be too complicated (at least, not MATH-wise. In terms of navigating the source code, I’m a fish out of water), I foresee shifting every vertex by some function of its distance from the threshold.
I like that idea, if I’m interpreting it correctly. But would it work from every angle? What if the viewing angle is perpendicular to the planes you describe?
This is what a lattice does, if I understand correctly what you mean. When you move the associated geometry through the (deformed) lattice, it stretches just like this.