Origami Theory and Its Applications: A Literature Review
This paper presents the fundamentals of Origami engineering and its application in nowadays as well as future industry. Several main cores of mathematical approaches such as Huzita- Hatori axioms, Maekawa and Kawasaki-s theorems are introduced briefly. Meanwhile flaps and circle packing by Robert Lang is explained to make understood the underlying principles in designing crease pattern. Rigid origami and its corrugation patterns which are potentially applicable for creating transformable or temporary spaces is discussed to show the transition of origami from paper to thick material. Moreover, some innovative applications of origami such as eyeglass, origami stent and high tech origami based on mentioned theories and principles are showcased in section III; while some updated origami technology such as Vacuumatics, self-folding of polymer sheets and programmable matter folding which could greatlyenhance origami structureare demonstrated in Section IV to offer more insight in future origami.
[1] Kanade, Takeo. "A Theory of Origami World." Artificial Intelligence,
1980: 280-311.
[2] Lang, Robert J. Origami Design Secrets - Mathematical Methods for an
Ancient Art. Massachusetts: A K Peters Ltd, 2003.
[3] Lang, Robert J. "TreeMaker User Manual." Langorigami. 2004.
www.langorigami.com (accessed Oct 15, 2009).
[4] Huzita-Hatori Axioms. Jan 31, 2009.
http://en.wikipedia.org/wiki/Huzita%27s_axioms (accessed Aug 10,
2009).
[5] Barile, Margherita, and Margherita Barile. "Kawasaki's Theorem." From
MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.
http://mathworld.wolfram.com/KawasakisTheorem.html (accessed Aug
30, 2009).
[6] Thomas C. Hull. Revisited and extended. Western New England College
http://courses.csail.mit.edu/ (accessed 10 September 2012)
[7] Tachi, Tomohiro. Rigid Origami Silmulation. TT's Page Research
Project. (Online) 2009. (Cited: Nov 5, 2009.)
http://www.tsg.ne.jp/TT/cg/index.html#rigid_origami
[8] Simulation of Rigid Origami. Tachi, Tomohiro. Tokyo : 4OSME, 2009.
[9] Kevin &Bobby, Saint Joseph's College. (Online) (Cited: Nov 5, 2009.)
www.saintjoe.edu/~karend/m111/Origami.ppt.
[10] KTK Scientific Publishers. "Map Fold a La Miura Style, Its Physical
Characteristics and Application to the Space Science", in Research of
Pattern Formation, edited by R. Takaki, pp. 77-90.
[11] Kitty Tinsley. 2003. A Giant Leap for Space Telescopes.Lawrence
Livermore National Laboratory https://www.llnl.gov/(accessed 10
August 2012)
[12] Origami-Resource-Center.com. Origami Science.
http://www.langorigami.com/science/technology/eyeglass/eyeglass.php
(accessed 5 August 2012)
[13] Zhong You, and Kaori Kuribayashi. 2003. A Novel Origami Stent.
Tulane University http://tulane.edu/ (accessed 10 August 2012)
[14] K. Kuribayashi and Z. You. Innovative Origami Expandable Stents.
University of Oxford http://www-civil.eng.ox.ac.uk/ (accessed 12
August 2012)
[15] University of Illinois at Urbana-Champaign. 2009. High-tech origami:
Water droplets direct self-assembly process in thin-film materials.
http://www.sciencedaily.com/releases/2009/11/091123152222.htm
(accessed 12 August 2012)
[16] University of Illinois at Urbana-Champaign. 2010. High-Tech Origami.
http://www.las.illinois.edu/news/2010/solarcell/ (accessed 12 August
2012)
[17] Zeeya Merali. 2011. Paper, Plastic, or Steel?.
http://news.sciencemag.org/sciencenow/2011/03/paper-plastic-orsteel.
html?ref=hp (accessed 15 August 2012)
[18] Bob Yirka. 2011. Origami solution found for folding steel shopping
bags. http://phys.org/news/2011-03-origami-solution-steel-bags.html
(accessed 15 August 2012)
[19] T. Tachi, M. Masubuchi and M. Iwamoto. 2012. Rigid Origami
Structures with Vacuumatics: Geometric Considerations. (accessed 5
August 2012)
[20] Hawkes, E. et al. Proc. Natl Acad. Sci. USA advance online publication
doi:10.1073/pnas.0914069107 (2010).
[21] Philip Ball. 2010. Origami that folds itself.
http://www.nature.com/news/2010/100628/full/news.2010.317.html
(accessed 15 August 2012)
[1] Kanade, Takeo. "A Theory of Origami World." Artificial Intelligence,
1980: 280-311.
[2] Lang, Robert J. Origami Design Secrets - Mathematical Methods for an
Ancient Art. Massachusetts: A K Peters Ltd, 2003.
[3] Lang, Robert J. "TreeMaker User Manual." Langorigami. 2004.
www.langorigami.com (accessed Oct 15, 2009).
[4] Huzita-Hatori Axioms. Jan 31, 2009.
http://en.wikipedia.org/wiki/Huzita%27s_axioms (accessed Aug 10,
2009).
[5] Barile, Margherita, and Margherita Barile. "Kawasaki's Theorem." From
MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.
http://mathworld.wolfram.com/KawasakisTheorem.html (accessed Aug
30, 2009).
[6] Thomas C. Hull. Revisited and extended. Western New England College
http://courses.csail.mit.edu/ (accessed 10 September 2012)
[7] Tachi, Tomohiro. Rigid Origami Silmulation. TT's Page Research
Project. (Online) 2009. (Cited: Nov 5, 2009.)
http://www.tsg.ne.jp/TT/cg/index.html#rigid_origami
[8] Simulation of Rigid Origami. Tachi, Tomohiro. Tokyo : 4OSME, 2009.
[9] Kevin &Bobby, Saint Joseph's College. (Online) (Cited: Nov 5, 2009.)
www.saintjoe.edu/~karend/m111/Origami.ppt.
[10] KTK Scientific Publishers. "Map Fold a La Miura Style, Its Physical
Characteristics and Application to the Space Science", in Research of
Pattern Formation, edited by R. Takaki, pp. 77-90.
[11] Kitty Tinsley. 2003. A Giant Leap for Space Telescopes.Lawrence
Livermore National Laboratory https://www.llnl.gov/(accessed 10
August 2012)
[12] Origami-Resource-Center.com. Origami Science.
http://www.langorigami.com/science/technology/eyeglass/eyeglass.php
(accessed 5 August 2012)
[13] Zhong You, and Kaori Kuribayashi. 2003. A Novel Origami Stent.
Tulane University http://tulane.edu/ (accessed 10 August 2012)
[14] K. Kuribayashi and Z. You. Innovative Origami Expandable Stents.
University of Oxford http://www-civil.eng.ox.ac.uk/ (accessed 12
August 2012)
[15] University of Illinois at Urbana-Champaign. 2009. High-tech origami:
Water droplets direct self-assembly process in thin-film materials.
http://www.sciencedaily.com/releases/2009/11/091123152222.htm
(accessed 12 August 2012)
[16] University of Illinois at Urbana-Champaign. 2010. High-Tech Origami.
http://www.las.illinois.edu/news/2010/solarcell/ (accessed 12 August
2012)
[17] Zeeya Merali. 2011. Paper, Plastic, or Steel?.
http://news.sciencemag.org/sciencenow/2011/03/paper-plastic-orsteel.
html?ref=hp (accessed 15 August 2012)
[18] Bob Yirka. 2011. Origami solution found for folding steel shopping
bags. http://phys.org/news/2011-03-origami-solution-steel-bags.html
(accessed 15 August 2012)
[19] T. Tachi, M. Masubuchi and M. Iwamoto. 2012. Rigid Origami
Structures with Vacuumatics: Geometric Considerations. (accessed 5
August 2012)
[20] Hawkes, E. et al. Proc. Natl Acad. Sci. USA advance online publication
doi:10.1073/pnas.0914069107 (2010).
[21] Philip Ball. 2010. Origami that folds itself.
http://www.nature.com/news/2010/100628/full/news.2010.317.html
(accessed 15 August 2012)
@article{"International Journal of Business, Human and Social Sciences:50696", author = "L. J. Fei and D. Sujan", title = "Origami Theory and Its Applications: A Literature Review", abstract = "This paper presents the fundamentals of Origami engineering and its application in nowadays as well as future industry. Several main cores of mathematical approaches such as Huzita- Hatori axioms, Maekawa and Kawasaki-s theorems are introduced briefly. Meanwhile flaps and circle packing by Robert Lang is explained to make understood the underlying principles in designing crease pattern. Rigid origami and its corrugation patterns which are potentially applicable for creating transformable or temporary spaces is discussed to show the transition of origami from paper to thick material. Moreover, some innovative applications of origami such as eyeglass, origami stent and high tech origami based on mentioned theories and principles are showcased in section III; while some updated origami technology such as Vacuumatics, self-folding of polymer sheets and programmable matter folding which could greatlyenhance origami structureare demonstrated in Section IV to offer more insight in future origami.
", keywords = "Origami, origami application, origami engineering,
origami technology, rigid origami.", volume = "7", number = "1", pages = "21-5", }
