I’m researching how to generate Origami tesselations and simulate them in Grasshopper. So far I’ve been able to simulate origami foldings in Kangaroo such as the Miura-Ori pattern. However, I recently stumbled upon a Japanese YouTube account with the most sophisticated origami calculations I’ve ever seen. Here is a link to one of his Origami’s https://www.youtube.com/watch?v=VeKFS0wpCig . Check it out, as well as his other videos, they are quite amazing! It seems that he is using Excel and Matlab to do his origamis, but the level of math is way beyond my understanding. What do you guys think? Is it possible in Grasshopper?

For simulating, these patterns shouldn’t pose too much difficulty - they don’t involve curved creases or a lot of stretching, so you could model them with Length constraints and hinges in the usual way.

Generating the crease patterns can be a bit more tricky though, since for it to be foldable the angles around each vertex need to meet more conditions than simple developability (summing to 2pi).

Thanks for the reply Daniel,

Simulating the folding is not the problem. I wonder if it’s possible to generate similar patterns on different surfaces and still have it be a functioning Origami geometry. He’s using some pretty complicated math

More specifically, for a vertex to be flat foldable, the sums of alternating angles around each vertex need to be equal.

Tomohiro Tachi has written several papers about this

https://tsg.ne.jp/TT/cg/index.html

For quad meshes where there are 4 faces around each vertex, this works out to be the same requirement as for conical meshes, which there is already a component for in Kangaroo.

By linking the edge lengths of a mesh you keep flat with a 3 dimensional one, you can ensure developability, then keep the quads planar and the vertices conical, and you can modify an almost foldable pattern into an actually foldable one.

Here’s one example:

flatfoldable.gh (16.9 KB)