Here a speed one about the above method
a little difficulty with your own object :it's very thin...
but you can with a bigger thin for understand the process to take the bottom curve (or any trimed curve) ;)
Project any curves from Top
erase the second bottom projection
Extrude the projected curves
Copy Move it out the volume for better view
Take the bottom Side line of your original Surf
maybe you must join its different part for have a unic curve
Rebuild it for have less points (select a curve Press Tab write Rebuild and enter your number of points)
movup a little in side view for drawing a cool triminng curve
Move some points to the extremities of the "any curves lines"
Extrude it for have a perpendicular plane
maybe Blend the Bottom curves for the background
and make some Boolean Diff of all that :)
Sorry for the masking pannel at the end, i am not in a comfortable place...for work!
All is here in 3 D view but of course change view (Left) for drawing or modify curves!
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