Upload File

lecture 1: linkages - massachusetts institute of …courses.csail.mit.edu/6.849/tokyo16/l02_slides -...

  • Home
  • Documents
  • Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
96
http://courses.csail.mit.edu/6.849/tokyo16/

Upload: vonhan

Post on 27-Apr-2018

218 views

Category:

Documents


1 download

Report

TRANSCRIPT

Page 1: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

http://courses.csail.mit.edu/6.849/tokyo16/

Page 2: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Page 3: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Hiden Senbazuru Orikata1797

Presenter
Presentation Notes
Scan of 1797 book
Page 4: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 16.2 from GFALOP
Page 5: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.1 of GFALOP
Page 6: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.9 of GFALOP
Page 7: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.12 of GFALOP
Page 8: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.7 of GFALOP
Page 9: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.13 of GFALOP
Page 10: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 12.16 of GFALOP
Page 11: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Flat Folding of Box-Pleated Crease Pattern is NP-complete

[Akitaya, Cheung,

Demaine, Horiyama, Hull,

Ku, Tachi, Uehara 2015]

Page 12: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Not-All-Equal 3SAT

• Given triples• Assign binary

values to variables so that every triple has both values

Page 13: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Not-All-Equal 3SAT

• Given triples• Assign binary

values to variables so that every triple has both values

Page 14: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Not-All-Equal 3SAT

• Given triples• Assign binary

values to variables so that every triple has both values

Page 15: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Not-All-Equal 3SAT

• Given triples• Assign binary

values to variables so that every triple has both values

Page 16: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Not-All-Equal 3SAT

• Given triples• Assign binary

values to variables so that every triple has both values

Page 17: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Graph Orientation

Page 18: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Graph Orientation

Page 19: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Bern & Hayes 1996]

Presenter
Presentation Notes
Figure 13.3 of GFALOP
Page 20: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya, Cheung, Demaine, Horiyama, Hull, Ku, Tachi, Uehara 2015]

Page 21: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Flat Folding of Box-Pleated Crease Pattern is NP-complete

[Akitaya, Cheung,

Demaine, Horiyama, Hull,

Ku, Tachi, Uehara 2015]

Page 22: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Flat Folding of Box-Pleated Crease Pattern is NP-complete

[Akitaya, Cheung,

Demaine, Horiyama, Hull,

Ku, Tachi, Uehara 2015]

Page 23: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya, Cheung, Demaine, Horiyama, Hull, Ku, Tachi, Uehara 2015]

Page 24: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Flat Folding of Box-Pleated Assigned Crease Pattern is NP-complete

[Akitaya, Cheung,

Demaine, Horiyama, Hull,

Ku, Tachi, Uehara 2015]

Page 25: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Flat Folding of Box-Pleated Assigned Crease Pattern is NP-complete

[Akitaya, Cheung,

Demaine, Horiyama, Hull,

Ku, Tachi, Uehara 2015]

Page 26: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

SODA 1996

Page 27: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya, Cheung, Demaine, Horiyama, Hull, Ku, Tachi, Uehara 2015]

true

true

true

true

[Bern & Hayes 1996]

≠

≠

Crossover is Broken

Page 28: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Electrabrake Manual FolderPress & Shear

Presenter
Presentation Notes
Frames from video http://www.youtube.com/watch?v=l_stw54dfZ4
Page 29: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Luxury and Elegant Home Design In The World / designinteriorart.comJuly 2011

Presenter
Presentation Notes
http://designinteriorart.com/wp-content/uploads/2011/07/unique-wall-decorating-with-various-functions.jpg and http://designinteriorart.com/wp-content/uploads/2011/07/wall-decorating-ideas-with-various-functions.jpg from http://designinteriorart.com/all-posts/decorating-wall-with-various-functions/
Page 30: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Sheetseat”Ufuk Keskin & Efecem Kutuk2009

Presenter
Presentation Notes
http://www.ufukkeskin.com/storage/sheetseat4.jpg from http://www.ufukkeskin.com/sheetseat/
Page 31: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Flat-Pack Furniture” dornob

Presenter
Presentation Notes
http://cdn.dornob.com/wp-content/uploads/2009/04/transforming-all-in-one-room-design3.jpg & http://cdn.dornob.com/wp-content/uploads/2009/04/transforming-fold-out-room-design2.jpg & http://cdn.dornob.com/wp-content/uploads/2009/04/transforming-modular-cardboard-room1.jpg from http://dornob.com/flat-pack-furniture-for-an-all-in-one-interior-design/
Page 32: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Folded Steel Design Furniture Ideas: Unique Coffee Table”Home Gallery Design October 2010

Presenter
Presentation Notes
http://homegallerydesign.com/wp-content/uploads/Modern-Furniture-Ideas-Unique-Coffee-Table.jpg & http://homegallerydesign.com/wp-content/uploads/Unique-Coffee-Table-Design-Furniture-Ideas.jpg & http://homegallerydesign.com/wp-content/uploads/Unique-Coffee-Table-Design-Folded-Steel.jpg & http://homegallerydesign.com/wp-content/uploads/Unique-Coffee-Table-Design-Home-Furniture.jpg from http://homegallerydesign.com/folded-steel-design-furniture-ideas-unique-coffee-table/
Page 33: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

SimpleFolds

[Akitaya, Demaine, Ku 2015]

Page 34: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

ModelAssigned Unassigned

One-layer NP-hard open poly open open poly

Some-layers NP-hard

NP-hard poly open NP-

hard poly

All-layers NP-hard

NP-hard poly open NP-

hard poly

InfiniteOne-layer

NP-hard open poly NP-

hard open poly

InfiniteSome-layers

NP-hard open poly NP-

hard open poly

InfiniteAll-layers open open poly open open poly

[Akitaya, Demaine, Ku 2015]

Page 35: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Arkin, Bender,

Demaine, Demaine, Mitchell,

Sethia, Skiena2000]

Presenter
Presentation Notes
Figure 14.5 of GFALOP
Page 36: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Arkin, Bender,

Demaine, Demaine, Mitchell,

Sethia, Skiena2000]

Presenter
Presentation Notes
Figures 14.5 and 14.6 of GFALOP
Page 37: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

3-Partition

• Given 𝑛𝑛 integers 𝑎𝑎1, 𝑎𝑎2, … , 𝑎𝑎𝑛𝑛, can you partition into 𝑛𝑛/3 triples with the same sum? 𝑡𝑡 = ∑𝑖𝑖 𝑎𝑎𝑖𝑖

⁄𝑛𝑛 3

This problem is strongly NP-complete:NP-complete even if 𝑎𝑎𝑖𝑖 numbers are 𝑛𝑛𝑂𝑂(1)

…?

𝑡𝑡

𝑛𝑛/3 triples

Page 38: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya,Demaine,Ku 2015]

Reduction from3-Partition

Page 39: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Reduction from3-Partition

[Akitaya, Demaine, Ku 2015]

Page 40: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya, Demaine, Ku 2015]

Page 41: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Akitaya,Demaine,Ku 2015]

Page 42: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Demaine, Demaine, Mitchell 1999]3D model byBitmapworld

Presenter
Presentation Notes
3D model from http://www.turbosquid.com/3d-models/3d-horse-animals-lightwave-model/269712 and rendered by Erik. Other drawings by Erik.
Page 43: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 15.4 of GFALOP
Page 44: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 15.2 from GFALOP
Page 45: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figures 15.2 and 15.3 from GFALOP
Page 46: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Tomohiro Tachi

Origamizer[Tachi 2006;

Demaine & Tachi2009–2016]

Presenter
Presentation Notes
Photos from http://graphics.stanford.edu/data/3Dscanrep/bunny-scanalyze-sh.jpg and http://www.flickr.com/photos/tactom/1003649096/ and http://www.flickr.com/photos/tactom/1002688931
Page 47: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Demaine & Tachi 2010

Presenter
Presentation Notes
From unpublished Origamizer paper by Erik Demaine & Tomohiro Tachi
Page 48: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

http://www.flickr.com/photos/tactom/

“Origamizer Screenshots for Hypar”Tomohiro Tachi, 2007

Presenter
Presentation Notes
Top image http://farm2.staticflickr.com/1208/1420669885_e335a62591_o.jpg from http://www.flickr.com/photos/tactom/1420669885/ distributed under Creative Commons Attribution-NonCommercial 2.0 License. Bottom image http://farm2.staticflickr.com/1018/1421577530_49be0f2b12_o.png from http://www.flickr.com/photos/tactom/1421577530/ distributed under Creative Commons Attribution-NonCommercial 2.0 License.
Page 49: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“3D origamibell shape”

Tomohiro Tachi2007

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Image http://farm2.staticflickr.com/1144/913624865_c0c90c4dbf_o.jpg from http://www.flickr.com/photos/tactom/913624865/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 50: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Mouse”Tomohiro Tachi

2007

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Image http://farm3.staticflickr.com/2399/2330200221_6b0f364462_o.jpg from http://www.flickr.com/photos/tactom/1476518003/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 51: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“3D mask”Tomohiro Tachi

2007

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Image http://farm2.staticflickr.com/1251/1476518003_1a816a5e0d_o.jpg from http://www.flickr.com/photos/tactom/2330200221/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 52: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Tetrapod”Tomohiro Tachi

2008

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Left image http://farm4.staticflickr.com/3003/2653269033_6fb887c21c_o.jpg from http://www.flickr.com/photos/tactom/2653269033/ distributed under Creative Commons Attribution-NonCommercial 2.0 License. Right image http://freeassociationdesign.files.wordpress.com/2010/09/2802993534_2de3ba2d37_b.jpg from http://freeassociationdesign.wordpress.com/2010/09/18/tetrapods-entropy-and-excess/
Page 53: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Leaf of Kajinoki(BroussonetiaPapyrifera)”

Tomohiro Tachi2007

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Image http://farm2.staticflickr.com/1261/1426795877_e4a33a5617_o.jpg from http://www.flickr.com/photos/tactom/1426795877/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 54: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Video: http://www.youtube.com/watch?v=GAnW-KU2yn4
Page 55: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“OrigamiStanfordBunny”

Tomohiro Tachi2007

http://www.flickr.com/photos/tactom/

Presenter
Presentation Notes
Image http://farm2.staticflickr.com/1284/1002688931_e2b6af10ab_b.jpg from http://www.flickr.com/photos/tactom/1002688931/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 56: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Metal Bunny

[Cheung, Demaine, Demaine, Tachi 2011]

Presenter
Presentation Notes
Video http://www.flickr.com/photos/tactom/5473218888/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 57: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Metal Bunny

[Cheung, Demaine, Demaine, Tachi 2011]

Presenter
Presentation Notes
Photo http://farm6.staticflickr.com/5292/5473218708_44294474ec_b.jpg from http://www.flickr.com/photos/tactom/5473218708/ distributed under Creative Commons Attribution-NonCommercial 2.0 License
Page 58: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Tree Method of Origami Design[Fujimoto, Kamiya, Kawahata, Lang, Maekawa, Meguro, Yoshino]

[Lang, Demaine, Demaine 2006–2016]

• Algorithm to fold optimal origami “base” with desired stick-figure projection

headforeleg

hindleg

tail

Page 59: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Tree Method of Origami Design[Fujimoto, Kamiya, Kawahata, Lang, Maekawa, Meguro, Yoshino]

[Lang, Demaine, Demaine 2006–2016]

• Algorithm to fold optimal origami “base” with desired stick-figure projection

headforeleg

hindleg

tail

Page 60: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Scorpion varileg, opus 379”Robert Lang, 2002

Presenter
Presentation Notes
Top colored figure is Figure 11.35 from Origami Design Secrets (1st edition), page 406. Tree is drawn by Erik. Bottom image http://www.langorigami.com/image.php?image=/art/arachnids/scorpion_varileg.jpg from http://www.langorigami.com/art/gallery/gallery.php?name=scorpion_varileg
Page 61: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Flying Grasshopper, opus 382”Robert Lang, 2003

Presenter
Presentation Notes
Top colored figure is Figure 11.36 from Origami Design Secrets (1st edition), page 407. Tree is drawn by Erik. Bottom image http://www.langorigami.com/image.php?image=/art/insects/flying_grasshopper.jpg from http://www.langorigami.com/art/gallery/gallery.php?name=flying_grasshopper
Page 62: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Alamo Stallion, opus 384”Robert Lang, 2002

Presenter
Presentation Notes
Top colored figure is Figure 11.37 from Origami Design Secrets (1st edition), page 408. Tree is drawn by Erik. Bottom image http://www.langorigami.com/image.php?image=/art/mammals/alamo_stallion.jpg from http://www.langorigami.com/art/gallery/gallery.php?name=alamo_stallion
Page 63: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Nazgul 7.3Jason Ku, 2007

Presenter
Presentation Notes
Images and design by Jason Ku. http://scripts.mit.edu/~jasonku/index.php?id=2007&model=nazgul2
Page 64: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Shrimp 1.8Jason Ku, 2006

Presenter
Presentation Notes
Images and design by Jason Ku. http://scripts.mit.edu/~jasonku/index.php?id=2006&model=shrimp1
Page 65: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Butterfly 2.2Jason Ku, 2008

Presenter
Presentation Notes
Images and design by Jason Ku. http://scripts.mit.edu/~jasonku/index.php?id=2008&model=butterfly1
Page 66: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Disk Packing for Origami Design

Page 67: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Disk Packing is NP-hard +𝑎𝑎𝑖𝑖

+𝑎𝑎𝑗𝑗

+𝑎𝑎𝑘𝑘

𝑎𝑎𝑖𝑖 + 𝑎𝑎𝑗𝑗+𝑎𝑎𝑘𝑘 = 𝑡𝑡

[Demaine, Fekete, Lang

2010]−𝑡𝑡

Presenter
Presentation Notes
Figures 10, 11, 2 of http://erikdemaine.org/papers/DiskPacking_Origami5/ (covered under MIT Faculty Open-Access Policy)
Page 68: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Wakoku Chiyekurabe — Kan Chu Sen, 1721

Presenter
Presentation Notes
“Wakoku Chiyekurabe” by Kan Chu Sen, published in 1721. Out of copyright. Scans by Erik Demaine. See http://erikdemaine.org/foldcut/sen_book.html
Page 69: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Wakoku Chiyekurabe — Kan Chu Sen, 1721

Presenter
Presentation Notes
“Wakoku Chiyekurabe” by Kan Chu Sen, published in 1721. Out of copyright. Scans by Erik Demaine. See http://erikdemaine.org/foldcut/sen_book.html
Page 70: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Kan Chu Sen (1721)

Presenter
Presentation Notes
Earliest known reference Precedes earliest origami reference!
Page 71: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Betsy Ross 1777”Jean Leon Gerome

Ferris, 1932

Harper’s New Monthly Magazine, 1873

Page 72: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

1922

Presenter
Presentation Notes
Where Martin Gardner heard of the problem
Page 73: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

1955

Presenter
Presentation Notes
Where Martin Gardner heard of the problem
Page 74: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 17.2 of GFALOP. See also http://erikdemaine.org/foldcut/examples/
Page 75: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 17.2 of GFALOP. See also http://erikdemaine.org/foldcut/examples/
Page 76: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 17.2 of GFALOP. See also http://erikdemaine.org/foldcut/examples/
Page 77: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 17.2 of GFALOP. See also http://erikdemaine.org/foldcut/examples/
Page 78: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Drawing by Erik Demaine & Martin Demaine. http://erikdemaine.org/foldcut/examples/
Page 79: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Jie Qi2010

Page 80: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Sarah Eisenstat2010

Page 81: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Jason Ku2010

Page 82: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 17.15 of GFALOP
Page 83: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 1 of http://erikdemaine.org/papers/SimpleFoldCut_CGGA2010full/
Page 84: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Figure 4 of http://erikdemaine.org/papers/MazeFolding_Origami5/ (covered under MIT Faculty Open-Access Policy)
Page 85: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Demaine, Demaine, Ku 2010]

Presenter
Presentation Notes
Figure 2 of http://erikdemaine.org/papers/MazeFolding_Origami5/ (covered under MIT Faculty Open-Access Policy)
Page 86: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Demaine, Demaine, Ku 2010]

Presenter
Presentation Notes
Made with http://erikdemaine.org/fonts/maze/
Page 87: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

[Demaine, Demaine, Ku 2010]

Presenter
Presentation Notes
Figure 4 of http://erikdemaine.org/papers/MazeFolding_Origami5/ (covered under MIT Faculty Open-Access Policy)
Page 88: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

folding by Christopher Chin

Presenter
Presentation Notes
Figure 4 of http://erikdemaine.org/papers/MazeFolding_Origami5/ (covered under MIT Faculty Open-Access Policy)
Page 89: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

http://erikdemaine.org/fonts/

Presenter
Presentation Notes
http://erikdemaine.org/fonts/maze/
Page 90: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP
Presenter
Presentation Notes
Class poster from http://courses.csail.mit.edu/6.849/fall12/poster_letter_lowres.pdf . Make your own make folding here: http://erikdemaine.org/fonts/maze/
Page 91: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Yes/No

Demaine,Demaine,

Stengle2011

Presenter
Presentation Notes
http://erikdemaine.org/prints/YesNo/
Page 92: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

Science/Art Demaine & Demaine, 2011

Presenter
Presentation Notes
http://erikdemaine.org/prints/ScienceArt/
Page 93: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

MartinGardner

Demaine,Demaine

2012

Presenter
Presentation Notes
http://erikdemaine.org/prints/MartinGardner/
Page 94: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

“Ralf Konrad'sRubik's Cube Tessellation”

Jorge Jaramillo/ georigami

January 2007

Presenter
Presentation Notes
Photo from http://www.flickr.com/photos/georigami/374615107/ distributed under Creative Commons Attribution 2.0 license
Page 95: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

AndyWilson

Presenter
Presentation Notes
Images http://www.spundreams.net/~andy/origami/tessellations/purple-octagons-merlin-uriel.jpg & http://www.spundreams.net/~andy/origami/tessellations/green-6-4-3-4-full.jpg & http://www.spundreams.net/~andy/origami/tessellations/orange-star-medium.jpg & http://www.spundreams.net/~andy/origami/tessellations/green-octagons-full.jpg & http://www.spundreams.net/~andy/origami/tessellations/orange-dark-detail-corner.jpg from http://www.spundreams.net/~andy/origami/tessellations.html
Page 96: Lecture 1: Linkages - Massachusetts Institute of …courses.csail.mit.edu/6.849/tokyo16/L02_slides - Origami.pdfHiden Senbazuru Orikata 1797. Scan of 1797 book. Figure 16.2 from GFALOP

TessAlex Bateman

Presenter
Presentation Notes
Software: http://www.papermosaics.co.uk/software.html Image: http://www.papermosaics.co.uk/Images/gui.gif

Senbazuru: A Prototype Spreadsheet Database Management System

ICEBERG Product catalogue ICEBERG...5185 Implant driver ISO 1797 CC/CC.I 3,5 S Implant driver ISO 1797 CC/CC.I 3,5 L Implant driver ISO 1797 CC/CC.I 4,1 S Implant driver ISO 1797 CC/CC.I

Proceso 1797

Mary Wollstonecraft Shelley (1797-1851)

SENBAZURU - Francois Laxalt

Novalis - Seleccion de Analectas-1797-179

20161018141741-0001...Diagnostic Reagents, Pharmaceutical Materials and Electronic Industrial Chemicals Harima Plant: 1543, Orikata, Alo-shi, Hyogo, 678-0254, Japan Manufacture of

2008 No. 1797 TRADE MARKS - Legislation

1797 (another source 1798)

Photo pleine page · origami creator who pays equal respect in his work to the classics of rhe past such as the Senbazuru Orikata, and the work of Frciclrich Froehel, as to the new

The Secret of One Thousand Cranes Origami - Hiden Senbazuru Orikata

Franz Schubert (1797 - 1828)

Franz Schubert(1797-1828)

Fwd: File: 10-1797-S16-Support Don't Waste LA Franchise Syclkrep.lacity.org/onlinedocs/2010/10-1797-S16_pc_3-30-14.pdfSubject: File: 10-1797-S16-Support Don't Waste LA Franchise System

GEORGE WASHINGTON 1789-1797

George Washington 1789 – 1797

Ar Treasury 1797

Prep for the Week Issue | 1797

Folding Paper Cranes for a Senbazuru

Presidential Biography George Washington 1789-1797

PDF (1797 KB) - World Bank eLibrary

1797-in001_-en-p 1797-TB3 and 1797-TB3S

John Adams’ Presidency 1797-1801

Reglamento de Aguas Catamarca 1797

President George Washington 1789–1797 & President John Adams 1797–1801 The Federalist Era 1789-1801

1797-in014_-en-p (1797-ACNR15).pdf

Barruil - The Antichristian Conspiracy (1797)

Growth and Division 1816-1832 Chapter 7. Presidential Review George Washington 1789-1797 George Washington 1789-1797 John Adams 1797-1801 John Adams 1797-1801

Napoleon s Ligurian Navy 1797-1814

George Washington Presidency 1789-1797

GEORGE WASHINGTON THE PRECEDENT PRESIDENT1789-1797

EXPEDIUM 5.5 Spine System - University of Iceland · 3 4 product cataloGue EXPEDIUM 5.5 Titanium Monoaxial Screws Cat. No Description Diameter Length 1797-02-425 1797-02-430 1797-02-435

J Immunol-2009-Chen-1797-803

Senbazuru Game

Utagawa Kuniyoshi 1797 - 1861