I believe that the PR is now ready for integration.

The two additional changes:

1. Using Simple_cartesian instead of Cartesian, and
2. Using GAL::Cartesian_coverter

will be done in a follow up PR.
I'd like to keep this one minimal, because there is another PR pending (implemented as part of GSoC), which relies on this one and already contains the changes of this one, and I would like to avoid conflicts as much as possible.

Originally posted by @efifogel in #9036 (comment)