slides for class 4 (pdf - 6.7mb)
TRANSCRIPT
![Page 1: Slides for Class 4 (PDF - 6.7MB)](https://reader030.vdocuments.net/reader030/viewer/2022020301/5868c4e31a28ab7f7d8b62aa/html5/thumbnails/1.jpg)
It's not clear to me that all of the examples (nazgul, scorpion, shrimp, etc.) are uniaxial. At least they don't seem to be. But I thought the algorithm you were describing worked only for uniaxial origamis?
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“Scorpion varileg, opus 379” Robert Lang, 2002
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Figure removed due to copyright restrictions. Refer to: Fig. 11.35–37 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 406–8.
Tree diagrams drawn by Erik Demaine.
Courtesy of Robert J. Lang. Used with permission.
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“Flying Grasshopper, opus 382” Robert Lang, 2003
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Figure removed due to copyright restrictions. Refer to: Fig. 11.35–37 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 406–8.
Tree diagrams drawn by Erik Demaine.
Courtesy of Robert J. Lang. Used with permission.
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“Alamo Stallion, opus 384” Robert Lang, 2002
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Figure removed due to copyright restrictions. Refer to: Fig. 11.35–37 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 406–8.
Tree diagrams drawn by Erik Demaine.
Courtesy of Robert J. Lang. Used with permission.
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John Montroll’s “Dog Base”
& “Sausage Dog”
folded by
Wonko, 2011
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How often is TreeMaker or Origamizer used in practice? What techniques are most commonly used for origami design?
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“Maine Lobster, opus 447” Robert Lang, 2004
7 Courtesy of Robert J. Lang. Used with permission.
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“Fiddler Crab, opus 446” Robert Lang, 2004
8Courtesy of Robert J. Lang. Used with permission.
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“C. P. Snow, opus 612” Robert Lang, 2009
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Courtesy of Robert J. Lang. Used with permission.
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“Emperor Scorpion, opus 593” Robert Lang, 2011
10 Courtesy of Robert J. Lang. Used with permission.
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“Pan 1.6” Jason Ku, 2007
Courtesy of Jason Ku. Used with permission.11
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“tessellated hypar”
Tomohiro Tachi 2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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“3D origami bell shape”
Tomohiro Tachi 2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.13
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“Mouse” Tomohiro Tachi
2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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“3D mask” Tomohiro Tachi
2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.15
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“Tetrapod” Tomohiro Tachi
2008
http://www.flickr.com/photos/tactom/
Photo courtesy of ash-man on Flickr. Used
with permission. License CC BY-NC-SA.
Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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“Leaf of Kajinoki (Broussonetia Papyrifera)”
Tomohiro Tachi 2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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To view video of folding the Stanford bunny, by Tomohiro Tachi: http://www.youtube.com/watch?v=GAnW-KU2yn4.
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“Origami Stanford Bunny”
Tomohiro Tachi 2007
http://www.flickr.com/photos/tactom/ Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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Metal Bunny
[Cheung, Demaine, Demaine, Tachi 2011] Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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Metal Bunny
[Cheung, Demaine, Demaine, Tachi 2011] Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.
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On boxpleating vs TreeMaker — is there something similar to TreeMaker for box pleating? Is the variety of trees that boxpleating can implement limited in some way?
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Cover and index image removed due to copyright restrictions.
Refer to: Lang, Robert J. Origami Design Secrets: Mathematical Methods
for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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Figure removed due to copyright restrictions.
Refer to: Fig. 13.32–39 from Lang, Robert J. Origami Design Secrets: Mathematical
Methods for an Ancient Art. 2nd ed. A K Peters / CRC Press, 2011, pp. 601–6.
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I'd like to see more of the triangulation algorithm
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I would like to understand better how the Lang Universal Molecule works.
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You mention a class of largely open problems where one tries to fold some 3D structure (such as a tetrahedron) optimally with a square of paper. Is there a name for this problem or some way to know what versions are open?
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For the checkerboard, you said we can efficiently get arbitrary flaps, but this doesn't look at all like a uniaxial base — how do we get from there to here?
Demaine, Demaine, Konjevod, Lang 2009
Courtesy of Erik D. Demaine, Martin L. Demaine, Goran
Konjevod, and Robert J. Lang. Used with permission.38
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tab
slots
Demaine, Demaine, Konjevod, Lang 2009 Courtesy of Erik D. Demaine, Martin L. Demaine, Goran Konjevod, and Robert J. Lang. Used with permission.
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Has anybody written software to take an image, sample at low resolution, and create the checkerboard-type folding pattern?
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.41
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.42
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.43
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.44
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.45
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.46
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.47
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.48
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Folding a Better Checkerboard [Demaine, Demaine, Konjevod, Lang 2009]
folding by
Robert Lang
Courtesy of Robert J. Lang. Used with permission.49
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[Demaine, Demaine, Konjevod,
Lang 2009]
“Wow, that was not one of the easier things I've done.” — Robert Lang
48 × 42
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How does the version of Origamizer that's actually in software but not proven work?
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http://www.flickr.com/photos/tactom/
“Origamizer Screenshots for Hypar” Tomohiro Tachi, 2007
Courtesy of Tomohiro Tachi. Used with permission. Under CC-BY-NC.52
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[Tachi 2010]
(A) (C)
P1
A1 A0
A4A3
A2
P4P3
P0P2
Voronoi diagram
P1
P0
A1
A0
B1
B0
(B)
Vertex-Tucking Molecule Edge-Tucking Molecule Surface Polygon
Image by MIT OpenCourseWare.
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Could you explain the tuck gadgets for the Origamizer a little more fully?
I was definitely very confused in the last few minutes with those diagrams with circles and spheres...
How do the tuck proxies work?
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MIT OpenCourseWarehttp://ocw.mit.edu
6.849 Geometric Folding Algorithms: Linkages, Origami, PolyhedraFall 2012
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.