Hello Valentine,
I'm happy that I was able to discuss the application a bit with you.
If you're ever planning on looking into the carving per level, then looking into the workings of 3d printing algorithms might also be useful.
It is up to a certain part the opposite of the carving per level (except for the fact that you cannot carve underneath your top surface).
The similarity lays (for me) in the fact that both need to define planes/regions to gradually build.
At your side you could define regions to gradually carve.
If it always goes back to zero depth after drawing a line, then maybe more complex approaches might not be that valuable.
If you ever need a sounding board or have questions, then don't hesitate to use the forum again.