
Algorithm generates practical paper-folding patterns to produce any 3D structure - edwinksl
http://news.mit.edu/2017/algorithm-origami-patterns-any-3-D-structure-0622
======
cr0sh
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 "protections" could be taken out for the method
and implementations.

But right now, all we have to "play with" 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 "universal", if nothing
else.

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?).

~~~
thomasahle
Given that both authors are pure mathematicians, rather than engineers, I
don't have the impression that they really care to monetize this. MIT could
possibly claim patents on their behalf though.

~~~
tracked24x7
> Given that both authors are pure mathematicians ..

Erik Demaine is a computer scientist:
[https://youtu.be/3e1ZF1L1VhY](https://youtu.be/3e1ZF1L1VhY)

~~~
eachro
theoretical computer scientist

~~~
AnthonBerg
That's the only type of computer scientist. Anything else is, say, a
programmer or a software developer. Which there is nothing wrong with.

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greydius
Check out [1] for videos of Erik Demaine's lectures on folding. Also, I highly
recommend the videos for the algorithms and data structures courses he's
taught/co-taught ([2] for example)

[1] [https://ocw.mit.edu/courses/electrical-engineering-and-
compu...](https://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-849-geometric-folding-algorithms-linkages-origami-polyhedra-
fall-2012/)

[2] [https://ocw.mit.edu/courses/electrical-engineering-and-
compu...](https://ocw.mit.edu/courses/electrical-engineering-and-computer-
science/6-851-advanced-data-structures-spring-2012/)

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teechap
Conference paper here:

[https://www.researchgate.net/publication/315747461_Origamize...](https://www.researchgate.net/publication/315747461_Origamizer_A_Practical_Algorithm_for_Folding_Any_Polyhedron)

~~~
mark_h
That is a spectacularly well-presented paper (and I haven't even attempted to
read it yet!). I love the visual overview of the algorithm in figure 3.

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specialist
Ages ago...

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 "templates", for
reuse, customization, etc.)

[https://en.wikipedia.org/wiki/Imposition](https://en.wikipedia.org/wiki/Imposition)

I'm now very curious if this general purpose origami algorithm can be used for
the same purpose.

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lovelettr
There was a really great NOVA episode, "The Origami Revolution" [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.

[1] [http://www.pbs.org/wgbh/nova/physics/origami-
revolution.html](http://www.pbs.org/wgbh/nova/physics/origami-revolution.html)

[2]
[http://www.pbs.org/video/2365955827/](http://www.pbs.org/video/2365955827/)

~~~
baldfat
NO! There is now a pay wall for me to view the videos! $5 or more more a month
donation levels.

Is this nation wide or only for my local area?

~~~
space_fountain
For what it's worth I got it too. Is this just for some content?

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jcl
A video of one of the authors folding a bunny model like the one in the
article:

[https://www.youtube.com/watch?v=GAnW-
KU2yn4](https://www.youtube.com/watch?v=GAnW-KU2yn4)

~~~
eltoozero
Excellent find, and I'd wager since it's one of the authors (Tachi) it _IS_
the bunny model from the paper.

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zitterbewegung
So this is a computer that is a 3D Paper Printer?

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] .

[1][https://en.wikipedia.org/wiki/Mathematics_of_paper_folding](https://en.wikipedia.org/wiki/Mathematics_of_paper_folding)
[2]
[https://en.wikipedia.org/wiki/Huzita%E2%80%93Hatori_axioms](https://en.wikipedia.org/wiki/Huzita%E2%80%93Hatori_axioms)

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pavel_lishin
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.

~~~
nerpderp83
You could use shape memory alloys to control join orientation, have one per
orientation at the joint and have the correct one "remember" to allow a
structure to reconfigure itself.

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sohkamyung
I was wondering what Robert Lang [1] makes of this. Looks like he approves of
it. _“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.”_

[1] [
[https://en.wikipedia.org/wiki/Robert_J._Lang](https://en.wikipedia.org/wiki/Robert_J._Lang)
]

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kadavero
Solving origami (2d) was the task of 2017 ICFP programming contest. I wonder
how this MIT approach would work for that task.

[http://icfpc2016.blogspot.com.au/2016/08/task-
description.ht...](http://icfpc2016.blogspot.com.au/2016/08/task-
description.html)

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GregBuchholz
Anyone have recommendations on: "How to Fold It: The Mathematics of Linkages,
Origami, and Polyhedra" by Joseph O'Rourke?

[http://howtofoldit.org/](http://howtofoldit.org/)

~~~
nerpderp83
Beautiful book, my copy came folded in half (I really appreciate what I hope
was an ironic FU from the Amazon drone).

It would make a great book around computational art, rapid prototyping,
kinematics, etc. The nice thing about origami is that it adds a physicality to
mathematics that makes it tangible and approachable.

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mmjaa
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?

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

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sdwisely
I'm guessing the difference between this and something like pepakura
([http://www.tamasoft.co.jp/pepakura-en/](http://www.tamasoft.co.jp/pepakura-
en/)) is it doesn't use cuts?

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Kequc
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.

~~~
kmill
No, they put a low-poly mesh into the algorithm (I presume so it'd be foldable
in a reasonable amount of time).

"Maybe links some of the triangles together" is the difficult part, especially
since they guarantee the boundary of the paper folds to the boundary of the
mesh.

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

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mendeza
Could this be applied to UV/texture mapping? I can see reversing the folding
would be really helpful to texture map more easily.

~~~
grondilu
I doubt it. In texture mapping cuts are allowed, so it is not origami.

~~~
colinthompson
Actually I think it could be quite relevant. The mere fact that origami
doesn't allow cuts is what makes this so attractive from a texturing
standpoint.

From what I can tell, it appears that there are many locations where the
original plane overlaps. If it is possible to easily calculate adjacency for
those triangles, you would be able to properly do filtering lookups.

Another question is how much overlapping there is. The more there is, the more
you potentially waste texture resolution.

Still, cool idea...

~~~
mendeza
That would be cool if there was any graduate students working on this topic. I
sure would like to work on a topic like this!

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rocky1138
Can we build homes of sheet metal with this?

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knicholes
I assume you're talking about more than just the metal. I can imagine the heat
transfer would be terribly high.

~~~
rocky1138
That's a great point. I hadn't considered that. What about paper homes? Highly
compressed cardboard, sprayed with a clearcoat afterward to make it
waterproof.

~~~
gerdesj
Joints will be your enemy! You might want some windows and doors for example.

What about a lower(ish) tech solution involving say wood and mud? My aunt and
uncle's previous house was largely that plus straw and (reed|straw) thatching
and was originally built in the 1630's. It's not a particularly old example
but one that springs to mind. We don't see many earthquakes, for example, here
nor many forest fires but that house has stood through at least one or two 1
in say 300 year weather events - not least a bit of a cold spell in the 18th C
and a few somewhat windy episodes.

That house has been patched up once or twice and I suspect that might be quite
hard with your paper/card jobbie. The clearcoat will probably discolour badly
and degrade within <10 years but obviously you could reapply it regularly.
Swallows and House Martens or similar might also nick bits of it for their
nests. I don't know what sort of insects you have to deal with where you are
but they could also get nasty with a paper abode 8)

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hyfgfh
Even Wams?

~~~
Traubenfuchs
If you can't make them yourself no algorithm will help you.

