Hi Romain,
Is there any plan to include this kind of computation in Boost Geometry?
At this moment geodesics not planned. However, as Mateusz said, we have the extension model so if it is somehow needed, it can be added extended functionality. As in my previous post, it can be implemented as an additional strategy
Another solution that I was thinking about - using Boost Geometry as it is right now - is to convert Geographic coordinates in Cartesian coordinates (it is possible to do that right?), Yes, it is possible.
and do the same kind of computation but based on Cartesian reference system (computation of distance, azimuth, and line should be easy). Would it be possible?
It is probably possible but I don't think it is the right way to do it. The geodesic calculation is a high accuracy calculation. As soon as you project to a Cartesian projection, you will loose that accuracy in the calculated distance. The same will be true for other properties as azimuth. Regards, Barend