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Very nice, especially the code for construction of the 4-in-1 weave.
There are 80 layer symmetry groups (Shubnikov and Koptsik, Symmetry in Science and Art, chapter 8). The European 4-in-1 weave looks like it belongs to the layer group pbmn.
It would be interesting to see to which layer groups the different known weaves belong, and also to design new weaves possessing the symmetry of unrepresented layer groups. The interlocking rings induce constraints on the allowed symmetries, so some layer groups cannot be represented.
Very fun project. I quickly got inspired and could not resist to try and make a shirt of some sort. Got quite far, but to have them perfect connect all the way is tricky. Perhaps easier if you include more rings (tens of thousands of rings)… Thanks for the inspiration!
So cool! This is exactly where I was planning to take this next, so it's very cool to see it implemented. And with nice styling to make it look like metal :-) Also-- love the use of RotatedTorus, that's a new one for me.
I think another thing to account for when making a shirt is the movement of the rings, since in theory the weave can "stretch" a certain amount. I kind of see that happening in your shirt model here, where at the neck the rings fit very close together and towards the hem of the shirt they seem farther apart. There is probably some measurable range of stretch that we can incorporate to give it a more realistic fit. And of course gravity has a hand in how this sits on a person as well... so many variables to account for!
Thank you for the reply!
Thanks! You can find the definition of RotatedTorus at the beginning of my notebook; it is an easy definition that uses the internal Torus object and rotates. For the styling you could even use the new MaterialShading to make it really look like metal.
Hi Isabel, nice post. If you want to make it more physical, it's not easy, but there are definitely options for doing so. One typical starting place, you may already know, is the hanging chain (see this article on the St. Louis Arch).
Another odd but interesting possibility--more related to SW current issues than wear-ability--would be to treat the links as a statistical mechanical system of interlinked "Hard Tori", then calculate dynamics using conservation of momentum and energy. Perhaps in so doing you could find something like phonon modes, but I don't know for sure if they would exist without elasticity (what allows something really to "stretch").
I think the dynamics problem would really be too hard because individual links are usually in contact with more than one other link. It will be ambiguous how to update states, not to mention that chain mail should have a lot of frictional damping. That damping also has the added practical consequence of making the armor difficult to move around in.
Anyways, dynamics is a totally different issue from finding a static least-energy configuration, which is all you need if the chain mail is just going to sit in a museum somewhere and never go into battle. In that case the catenary problem already has all the essential physical principles. Larger problems can possibly be solved numerically by stochastic search procedure which looks like calculus of variations from an incremental perspective.
Have you tried using Key-Rings to physically build different sheet patterns?
They're quite cheap and are available on Amazon or eBay.
I did this many years ago and still have one or two test sheets left!