That video shows a very specific and unusual type of gridshell - where the laths are oriented with their large dimension normal to the shell.
These asymptotic gridshells are a quite recent development. Eike Schling in particular has been working focused on these over the last few years. See here for one of his publications on this.
In conventional actively bent timber gridshells, the laths are usually wider than they are deep, and layered instead of intersecting, with a connection where they cross which allows them to rotate. They start with the members unstressed in the flat state, and have to be pushed or pulled up:
If you are just interested in getting started with gridshells in general, then I’d recommend looking at this type to begin with, as they have been around much longer, with plenty of large scale built examples and lots of literature about them.
In asymptotic gridshells instead the members have to be already under significant bending in the initial flat grid, and as the shell pops up, this bending turns into twisting.
One key characteristic of these is that if you want to be able to use laths which are straight in their unstressed state, the grid has to follow the asymptotic directions of a minimal surface.
Which way round are you looking to work with these? A tool for actually designing them from the 3d first, then down to the flat intersection pattern, or something where you can start with various flat grids and see what shapes they pop up into?
You talk about 3d printing though, which would be very different to what is shown in the video, since if you print an asymptotic gridshell in the flat state, not only would the joint angles not be able to change, but the bending stress would not be there, so it would not pop up like the one in the video.