you refer to a result from L2 that you can determine in ...courses.csail.mit.edu/6.849/fall12/lectures/C03_images.pdfScans of Toshikazu Kawasaki’s “On High Dimensional Flat Origamis”,

[…] you refer to a result from L2 that you can determine in linear time whether something folds flat. Is this referring to the mingling algorithm? I haven't thought about this in detail, but it appears to take something like quadratic time […]

I was a tad confused on the local foldability algorithm. An example in class actually running the algorithm would probably clear it up.

Can you clarify what you mean by a path or cycle?

PresenterPresentation NotesFigure 13.1 of GFALOP

PresenterPresentation NotesFigure drawn by Erik

>360° cones could be made by fabric — perhaps you want to fold a garment along its seams, but the seamed sections meet in a point and the sum of the angles is greater than 360° (e.g., underarm of a shirt)

PresenterPresentation NotesImage from http://www.freemania.net/images/free-custom-shirt.jpg

“Japanese way of folding T-shirts!” mushk45 June 2006 youtu.be/b5AWQ5aBjgE

PresenterPresentation NotesVideo from http://www.youtube.com/watch?v=b5AWQ5aBjgE

“T-Shirt Folding Machine” gotcsin February 2008 youtu.be/rMnNHA_GrT8

PresenterPresentation NotesVideo from http://www.youtube.com/watch?v=rMnNHA_GrT8See more machines: http://www.core77.com/blog/object_culture/t-shirt_folding_machines_from_diy_to_industrial_19420.asp

If flat foldability is to fold a 2D sheet of paper in 2 dimensions, are there results for “flat foldability” in higher dimensions, i.e. to fold a d-dimensional sheet of paper in d dimensions? Can the result be generalized to higher dimensions?

PresenterPresentation NotesScans of Toshikazu Kawasaki’s “On High Dimensional Flat Origamis”, in Proceedings of the First International Meeting of Origami, Science and Technology, 1989.

PresenterPresentation Noteshttp://www.art-science.org/journal/v4n4/v4n4pp151/artsci-v4n4pp151.pdf

simple fold

inside reverse

fold simple

fold


We've spent a good chunk of time talking about flat foldability. What is the significance to this? Why is so much work done coming up with proofs and algorithms regarding this?

“Ralf Konrad's Rubik's Cube Tessellation”

Jorge Jaramillo

/ georigami

January 2007

PresenterPresentation NotesPhoto from http://www.flickr.com/photos/georigami/374615107/ distributed under Creative Commons Attribution 2.0 license

[EASi Engineering]

Airbag Folding

[BRL Inc]

creases based on computational origami design

PresenterPresentation NotesEASi Engineering (top) images from animation http://langorigami.com/science/technology/airbag/airbag.mov from http://langorigami.com/science/technology/airbag/airbag.php

PresenterPresentation Noteshttp://www.tsg.ne.jp/TT/cg/RigidFoldableQuadMeshOrigami_tachi_IASS2009.pdf

Miura-ori

perturbation of Miura-ori

freeform Miura-ori

PresenterPresentation Noteshttp://www.tsg.ne.jp/TT/cg/RigidFoldableQuadMeshOrigami_tachi_IASS2009.pdf

[…] you refer to a result from L2 that you can determine in linear time whether something folds flat. Is this referring to the mingling algorithm? I haven't thought about this in detail, but it appears to take something like quadratic time […]I was a tad confused on the local foldability algorithm. An example in class actually running the algorithm would probably clear it up. Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7>360° cones could be made by fabric — perhaps you want to fold a garment along its seams, but the seamed sections meet in a point and the sum of the angles is greater than 360° (e.g., underarm of a shirt)Slide Number 9Slide Number 10If flat foldability is to fold a 2D sheet of paper in 2 dimensions, are there results for “flat foldability” in higher dimensions, i.e. to fold a d-dimensional sheet of paper in d dimensions? Can the result be generalized to higher dimensions?Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17We've spent a good chunk of time talking about flat foldability. What is the significance to this? Why is so much work done coming up with proofs and algorithms regarding this?Slide Number 19Airbag FoldingSlide Number 21Slide Number 22

Documents

you refer to a result from L2 that you can determine in ...courses.csail.mit.edu/6.849/fall12/lectures/C03_images.pdfScans of Toshikazu Kawasaki’s “On High Dimensional Flat Origamis”,