Algorithm generates practical paper-folding patterns to produce any 3D structure

I hope the algorithm becomes published and unencumbered by any onerous restrictions. I understand that this is a unique system, though - and likely one where patents and other &quot;protections&quot; could be taken out for the method and implementations.<p>But right now, all we have to &quot;play with&quot; is a window binary. I understand that there is supposed to be a paper published in the future; I would love to see this algorithm implemented into something more &quot;universal&quot;, if nothing else.<p>Again, though, I can also see why such an algorithm could be protected - I am certain there are more than a few commercial applications for it, and perhaps in areas that have little to nothing to do with origami (for instance - and I am probably completely off base here - could this be applied in some manner to understanding protein folding?).

Check out [1] for videos of Erik Demaine&#x27;s lectures on folding. Also, I highly recommend the videos for the algorithms and data structures courses he&#x27;s taught&#x2F;co-taught ([2] for example)<p>[1] <a href="https:&#x2F;&#x2F;ocw.mit.edu&#x2F;courses&#x2F;electrical-engineering-and-computer-science&#x2F;6-849-geometric-folding-algorithms-linkages-origami-polyhedra-fall-2012&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ocw.mit.edu&#x2F;courses&#x2F;electrical-engineering-and-compu...</a><p>[2] <a href="https:&#x2F;&#x2F;ocw.mit.edu&#x2F;courses&#x2F;electrical-engineering-and-computer-science&#x2F;6-851-advanced-data-structures-spring-2012&#x2F;" rel="nofollow">https:&#x2F;&#x2F;ocw.mit.edu&#x2F;courses&#x2F;electrical-engineering-and-compu...</a>

Conference paper here:<p><a href="https:&#x2F;&#x2F;www.researchgate.net&#x2F;publication&#x2F;315747461_Origamizer_A_Practical_Algorithm_for_Folding_Any_Polyhedron" rel="nofollow">https:&#x2F;&#x2F;www.researchgate.net&#x2F;publication&#x2F;315747461_Origamize...</a>

Ages ago...<p>I wrote print production (prepress) software. One of my inventions was an algorithm that converted book binding steps into impositions, as needed. (All previous solutions relied on catalogs of manually created &quot;templates&quot;, for reuse, customization, etc.)<p><a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Imposition" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Imposition</a><p>I&#x27;m now very curious if this general purpose origami algorithm can be used for the same purpose.

There was a really great NOVA episode, &quot;The Origami Revolution&quot; [1][2], that I believe covered this exact same algorithm. As I recall at the time of the recording for the NOVA episode it was still under development.<p>[1] <a href="http:&#x2F;&#x2F;www.pbs.org&#x2F;wgbh&#x2F;nova&#x2F;physics&#x2F;origami-revolution.html" rel="nofollow">http:&#x2F;&#x2F;www.pbs.org&#x2F;wgbh&#x2F;nova&#x2F;physics&#x2F;origami-revolution.html</a><p>[2] <a href="http:&#x2F;&#x2F;www.pbs.org&#x2F;video&#x2F;2365955827&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.pbs.org&#x2F;video&#x2F;2365955827&#x2F;</a>

A video of one of the authors folding a bunny model like the one in the article:<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=GAnW-KU2yn4" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=GAnW-KU2yn4</a>

So this is a computer that is a 3D Paper Printer?<p>Jokes aside [1] the mathematics of paper folding is extremely interesting. The most interesting thing is that you can solve fourth degree equations with origami [2] .<p>[1]<a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Mathematics_of_paper_folding" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Mathematics_of_paper_folding</a> [2] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Huzita%E2%80%93Hatori_axioms" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Huzita%E2%80%93Hatori_axioms</a>

The science-fiction fan in me is now imagining a robot whose structure is a flat sheet of material, that can reconfigure itself into any form it needs.

I was wondering what Robert Lang [1] makes of this. Looks like he approves of it. <i>“It’s very impressive stuff,” says Robert Lang, one of the pioneers of computational origami and a fellow of the American Mathematical Society, who in 2001 abandoned a successful career in optical engineering to become a full-time origamist. “It completes what I would characterize as a quest that began some 20-plus years ago: a computational method for efficiently folding any specified shape from a sheet of paper. Along the way, there have been several nice demonstrations of pieces of the puzzle: an algorithm to fold any shape, but not very efficiently; an algorithm to efficiently fold particular families of tree-like shapes, but not surfaces; an algorithm to fold trees and surfaces, but not every shape. This one covers it all! The algorithm is surprisingly complex, but that arises because it is comprehensive. It truly covers every possibility. And it is not just an abstract proof; it is readily computationally implementable.”</i><p>[1] [ <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Robert_J._Lang" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Robert_J._Lang</a> ]

Solving origami (2d) was the task of 2017 ICFP programming contest. I wonder how this MIT approach would work for that task.<p><a href="http:&#x2F;&#x2F;icfpc2016.blogspot.com.au&#x2F;2016&#x2F;08&#x2F;task-description.html" rel="nofollow">http:&#x2F;&#x2F;icfpc2016.blogspot.com.au&#x2F;2016&#x2F;08&#x2F;task-description.ht...</a>

Anyone have recommendations on: &quot;How to Fold It: The Mathematics of Linkages, Origami, and Polyhedra&quot; by Joseph O&#x27;Rourke?<p><a href="http:&#x2F;&#x2F;howtofoldit.org&#x2F;" rel="nofollow">http:&#x2F;&#x2F;howtofoldit.org&#x2F;</a>

I would love to use this to build airfoils and flying devices .. anyone had a chance to play with it? Is it feasible to import a plane model, and end up with a 3D paper airplane like never seen before?

would be amazing to see the Rubic&#x27;sCube and Chess speed solvers burn this algorithm into their heads and start a competition to replicate a provided item.

I&#x27;m guessing the difference between this and something like pepakura (<a href="http:&#x2F;&#x2F;www.tamasoft.co.jp&#x2F;pepakura-en&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.tamasoft.co.jp&#x2F;pepakura-en&#x2F;</a>) is it doesn&#x27;t use cuts?

It looks like it just goes low-poly, all triangles as is pretty normal. Then maybe links some of the triangles together, ultimately telling you how many paper triangles how many different sizes to make.

Thanks for sharing this article. It was an interesting read about the progression of the idea into the tool available. I&#x27;m going to try out the software when I get a chance.

Could this be applied to UV&#x2F;texture mapping? I can see reversing the folding would be really helpful to texture map more easily.

Can we build homes of sheet metal with this?

Even Wams?