This video collects some of my recent geometrical play in Rhino/Grasshopper. I’ll be posting further explanations and definition files here over the next few days. Among the things shown are:

Continuing to explore corrugations which are rigidly foldable – ie. there is no deformation of the faces during the folding process.
This has links to some surprisingly deep mathematics – in particular the subjects of discrete differential geometry and integrable structure – Which have important architectural applications (such as finding planar panelings of curved surfaces) and also tie in with my earlier interest in minimal surfaces and circle packings.

The same principles can be naturally extended to other piecewise-planar surfaces such as the one above, which is rigidly foldable but does not unfold to flat.

Inspired and informed by the work of Tom Hull and Tim Hoffmann

My electric field sketch in Grasshopper controlling the metamorphosis of the MARS double corrugation pattern. Folded in Rigid Origami Simulator

Andrew Hudson has been making some beautiful curved-fold origami using grids from my recent work with electric fields:

I’m really looking forward to seeing how this develops.

While we’re on the subject of origami…    (video)

I made this using Tomohiro Tachi‘s brilliant ‘Rigid Origami Simulator’ (He has some other great stuff on his Flickr)
You can see physical versions of the same corrugations in my earlier deployables vid.
Here are the patterns:

Numbers 3 and 6 were found in the 60s by Ron Resch.
I think number 4 was first done by John Mckeever and 2 and 5 by Ben Parker

The ‘bricklaying’ style number 2 in particular seems promising to explore further. It has a nice volumetric quality when fully folded and feels quite strong. It looks like it could be easily adjusted to give different curvatures.

I was thinking these corrugations might work well as the core in a (curved) structural sandwich panel. I wonder, is anybody already doing this sort of thing?

-update
just found an example of this sort of ‘industrial origami’ here: Tessellated Group

Next step would be to combine it with something a bit like this pattern for variable curvature (by Tomohiro Tachi again).

Of course you would need to fold the linerboard as well, or use multiple strips. But doubly curved sandwich panels – Surely that could be really useful for all sorts of things!