Hi Sergio --

Thanks for taking a look at the Q-ray coordinates! 

You're right about many bridges to crystallography in this neighborhood.

​I'm part of a tiny subculture that came up with Q-rays in a listserv long ago. 

http://mathforum.org/library/view/6236.html

It's not that I'm the only one familiar with the ideas or that I'm the only contributor, just I know of no one else bringing it to the attention of a pre-college class, and I do that only rarely.

The connection with Python is a Quadray class is implemented therein.  My friend Tom has them in C++ (see Wikipedia). 

https://github.com/4dsolutions/Python5/blob/master/QuadraysJN.ipynb

I've also dabbled in a Clojure version.

https://github.com/4dsolutions/synmods/blob/master/qrays.clj

I worked with Quaternions a long time ago, to do a rotating cube applet, but then applets became a deprecated technology, much to everyone's surprise and consternation.

http://4dsolutions.net/ocn/oopalgebra.html

Kirby
​

On Tue, Jun 19, 2018 at 12:14 PM, Sergio Rojas <sergio_r@mail.com> wrote:
 
Kirby,

Looking way far in the back of my head,
the closest thing (to the inspirational drawings of
your notebook) I could recover
is what is called fundamental lattice structures of
solid state physics. Not sure, but in there
they might use your coordinate system to better describe
structures of crystals.
The book by Kittel, pg 27 of the 8th Edition, has some stuff on it.

Other object in that sense is the Quaternion thing
  https://en.wikipedia.org/wiki/Quaternion

Better stop here, I am getting hurt ...

Sergio