My request, turns out, is much simpler than I initially thought it would be.
I only need to do this sweeping thing with a primitive cylinder. I have seen
some applications applying boolean in over a 100 cylinders translated by a
few millimeters (meaning it's virtually a discrete "extruding", which would
have the desired result for me).
CGAL allows for such operations, but since I've been trying it with
triangles, you can image very slow booleans, minutes long, while the other
apps execute such "swept" in just about a second.
I've recently come across the Nef_polyhedron and I'm optimistic that it will
allow me to generate something cleaner using much less data crunching
algorithms. Am I on the right track, or CGAL is not the solution for this