Description: I want to push one mesh into another mesh and have it deform in the most simple way possible that is still animateable in some form (through a empty or something).
Example:
Lets say I have a simple plane (in this case with solidify so you can actually see it) and a cylinder below it:

I now move the cyclinder up a bit and it deforms the plane. This is easy to do in various ways:

Now the part I struggle with: If I now move the cylinder to the right I want the plane to keep deforming WITHOUT dragging half the mesh after it:

Problem: I am looking for a solution to do this WITHOUT soft bodies (it is extremly finicky, unperformant and seems to be quite overblown for something this simple. I also would like to have full control over the result) or a hundred shape keys that allows me to animate it (thinking about binding the cylinder to a bone).
Another example that comes to mind would be squeezing something through a hose, like in comics.
Any solutions or do I have to do with soft bodies?
I'll have a try with the warp modifier, I tried it with a lattice already but I can't figure out a way to make it "move" without essentially animating every single lattice vertex. Thanks for the suggestions!
Edit: While writing that the cylinder is not even required it just occured to me that I could probably do something with a custom displacement texture.
– Marcus Sep 02 '21 at 14:16