This is a nice tutorial, but it seems a bit kludgey (and I'm guessing part of that is due to Fusion 360's "not quite a fully finished CAD system," though they are making pretty good progress with it, and I find it's a fairly nice program, especially for the price, (free to hobbyists) and it includes CAM abilities.)

I would think OpenSCAD would be pretty decent at this, but honestly, I've never tried making parabola's or similar with it.

A quick google found this openscad script for parabolas: http://www.thingiverse.com/thing:84564

If you had a specific design in mind, it might actually be more satisfying to generate the STL triangles directly. You can fit your parabola in 2D (by, say, computing reflection angle to a fixed focal point), then just rotate and dump out STL.

The wiki has a nice intro to the subject:

https://en.wikipedia.org/wiki/Parabolic_reflector

Alternatively, one could use the "define curve by equations" feature. Most CAD tools have it.

ok for the 3d printing of the "structure" but then how to make it reflective? do you use regular allumination chamber or what technique ? which precision you can achieve to validate the prototype ?

I've had outstanding luck with this paint (1).

Print your model in ABS. Smooth it by putting it in a paint can on a little stand with some acetone soaked rags below for about 1/2 hour. Paint with some of this paint. You will be amazed.

(1) https://www.amazon.com/Krylon-1010A-Premium-Metalic-Original...

Obviously it's for a metal 3d printer...

I don't think so. The cost would be extremely prohibitive. It would be far cheaper to print it in plastic and then add some reflectie coating.

Most metal 3d printers simply don't have the surface finish to make this feasible, never mind cost (it'd be ridiculous).

I guess i should have added a ;-).

Although the laser sintering printer downstairs produces quite nice surface finishes. Not good enough for an optical mirror, but definitely good enough for mm-wave antennas.