Geometric Folding Algorithms: Linkages, Origami, Polyhedra | Hacker News Reader

Geometric Folding Algorithms: Linkages, Origami, Polyhedra

ocw.mit.edu

122 pointstodsacerdoti19 comments

Cool links from syllabus:

Origami Simulator: http://www.tsg.ne.jp/TT/software/index.html

Treemaker: https://langorigami.com/article/treemaker/

You forgot http://apps.amandaghassaei.com/OrigamiSimulator/ And maybe https://rabbitear.org

This intereste me because I've been looking at folding and unfolding of programs recently for some bit of fun work on the side of my PhD (or maybe not so on the side). I was looking for easy examples of this thing online and this is the closest I could find:

https://www.cs.kent.ac.uk/projects/refactor-fp/catalogue/Fol...

  -- Folded program
  showAll = (concat . format) . map show
  table   = concat . format

  -- Unfolded program
  showAll = table . map show
  table   = concat . format

I've been wondering if there is maybe some kind of correspondence between programming and geometry in this respect. In the context of programming "folding/unfolding" is just an analogy and one has to stare at examples like the one above for a bit to appreciate how apt it is, whereas it's much more obvious to see when it comes to geometry. Also, the programming term signifies replacement of a structure by another, whereas folding geometric objects is, I think, not really a replacement. But, well, this thing is now stuck in my mind.

There is a lot of correspondence. I was recently working on making a "geometry" based programming language. As I was working through it one of the ideas I realized geometry was a really good fit for was a language focused on pattern matching and data deduplication.

There is an origami-focused, peer-reviewed academic conference "OSME" and the papers that have come out of it (released in books) are interesting reads.

The conference website is http://osme.info/ (hasn't been updated in a while; see Robert Lang's page for more info: https://langorigami.com/article/origami-conferences/)

Anyone know if this field has gained any substantial traction since 2012 and the collaborations with NASA? Looks really interesting, but seems more recreational, though i could be wrong.

If you look at the later lectures, it seems the recreational aspects are a trap to get you to attend thing like: ”Algorithms for unfolding 2D chains, pseudotriangulation, energy; rigid folding of single-vertex origami; locked trees, infinitesimally locked linkages, Rules 1 and 2; locked 3D chains, knitting needles.” Here you are fairly far from ’recreational’ folding, those words paint pictures of serious people gettin very upset at the very notion of folding something for pleasure!

http://courses.csail.mit.edu/6.849/fall12/lectures/

Although I think some of those algorithms have led to the creation of software that is used by people folding recreationally.

He talks about applications in the first lecture:

* Robotics is a big one, folding robotic arms.

* Computer graphics. ... animate your characters ... skeletons as foldable objects

* Mechanics: A lot of the early folding work is in like 17, 1800s, and is motivated by building mechanical linkages to do useful things.

* Manufacturing: if you could get them to fold objects (ex: CPUs), then you could manufacture 3D nano-scale objects.

* Optics. A MIT group does some optical devices through folding

* Medical: folding a stent really small, do non-intrusive heart surgery. Drug delivery.

* Aero-astro. fold things within space shuttles

* Biology. Big one: protein folding

* Sculpture: origami.

* Interactive buildings' architecture: reconfigurable buildings. Hoberman is one example of somebody exploring this, getting the building to fold from one shape to another, or getting your shades to fold from one shape to another, all sorts of things.

What about parachutes?

Well he doesn't discuss parachutes... What would be an improvement in this case? I guess one could came up with a smaller parachute if it was optimally folded.

Psychologically I suspect I would feel safer with a regular size parachute vs a super advanced, algorithmically folded origami-parachute :-p

I never got as far as folding my own parachute, but I know they have to be folded somehow, and if it doesn't unfold properly, you die (modulo the reserve). So I'd speculate optimization could have a role in reliability. My memory is hazy, but I may have been told that the method of folding also affects how abruptly and with how much shock it opens.

https://twitter.com/littmath/status/1291484760875966467

You can't go wrong with any of Erik Demaine's classes.

When I taught an algorithms course, Erik's 6.006 and 6.046 lectures were one of my main sources for lesson plans and other inspiration.

Isn't there a documentary about this guy? It looks so familiar.

You're probably thinking about https://www.imdb.com/title/tt1253565/?ref_=nm_ov_bio_lk3

You're probably thinking of the documentary Between the Folds.

He's appeared in a lot of places though. Really interesting guy: homeschooled by his father in a van, finished his PhD before many people finish their second year of undergrad, youngest ever professor hired at MIT. Tons of mindblowing papers on computational origami.

I wish Erick made an edx course

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