Hi Pilou, attached here is a finished result.

> you can't extrude because bow and poop are inversed inclined!

Then simply do an extrusion which creates the proper edge direction in the back, and slice the result with a line in the front to cut it to the desired angle.

The attached result is an extrusion so you may need to cut it with a line (since it is a solid use the boolean difference for cutting it) to get the proper angle. But other than that it seems to be all set up.

The untrimmed original surface was not quite large enough to cover the offset curves completely, so I extended it by adding a tangent line to either side and extruding it.

- Michael