How to design parabolic, hyperbolic, elliptical reflectors for 3D printing

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 ?