Would you be willing to explain what the applications of (2) are? I'll admit that I only undersetand a fraction of what you said in that section, but I'm curious what you're using it for.
Sure: the automated design-by-optimization of ship hull form geometry which meets constraints and is smooth according to some energy measures.
Build a functional to describe your ship problem, minimize it: if the solver is happy, you have a boat.... uh, or if you haven’t solved the entire problem, you have some geometry which can be stitched together with more optimization to make a boat.
More broadly, “why a boat?”
Answer: because boats have a lot of constraints, and a lot of shape ( Gaussian curvature, non rectangular topology, a need to be cheaply produced, etc etc)
So it’s a good problem to tax your generative design or design space search/optimization capability.
