The Kogod courtyard and other turtle's shell- diagonal grid as a roof structure

Let's say you want to design a wide roof, that has a dynamic and lively look.
A good example would be the Kogod courtyard of the Smithsonian American Art Museum, By Foster & partners, Smith group Inc. Buro Happold, Sandy Brown Associates, or the Mediacite by Ron Arad.

I challenged myself to understand this kind of structure, using my modest means and limited time, up to the point of being able to design a diagrid curved roof, as if I indent to order the peaces in a DIY store and put it together. By the way: this proved a tricky process!
Anyway, here are my "findings"-

The basic act to do is to apply a diagrid on a 2-way curved surface.
I began with a simple gird, symmetric in to ways:

Then I used an arc to define the first direction of the roof surface (and allowed myself to skip the question of a curved surface for now).

I used the grid and the arc to define the other direction of the roof plane - a series of profiles made of more arcs:

Now the "problem" is already solved: each member of the roof elements is determined: X & Y values are based on the basic grid, and Z value is determined by interesting the grid point with the arc over it:

The diagrid can be formed in an act of "sewing":

And mirrored on the symmetrical grid.

The final result is, as promised, a diagrid applied on a two- way curved surface- a little like a turtle's shell.

Some more questions emerged while doing this trick:
How to define a surface with curves instead of arches - that's what gives so much beauty to Kogot courtyard and such roofs; What 3D software would you use to design such a roof? and, of course, how to detail this system in order to actually be able to build it?
If you have any ideas or thoughts, please leave a comet!

Until the next time,
Yours truly,
The virtual architect