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abstract

Lang's universal molecule algorithm

Published: 17 June 2012 Publication History

Abstract

We present a Java implementation of Lang's Universal Molecule algorithm, alongside with a visualization of its interconnected structures: the input metric tree and compatible convex polygon, whose 2D crease pattern and 3D uniaxial base are computed by the algorithm. The Java applet, the video, as well as further references and accompanying materials are available on our web site http://linkage.cs.umass.edu/origamiLang. We also include a recent example, found with the help of this implementation, of a Universal Molecule crease pattern which, as a flat-faced origami, is completely rigid; in particular, its corresponding uniaxial base cannot be reached through continuous folding without bending of the paper.

References

[1]
J. C. Bowers and I. Streinu. Lang's universal molecule algorithm. Technical report, Dec 2011.
[2]
J. C. Bowers and I. Streinu. Rigidity of Lang's origami universal molecules. Technical report, Feb 2012. (Submitted).
[3]
R. J. Lang. Origami design secrets: mathematical methods for an ancient art, A. K. Peters, 2003.
[4]
R. J. Lang. A computational algorithm for origami design. In Proceedings of the 12th Annual ACM Symposium on Computational Geometry, pages 98--105, 1996.
[5]
R. J. Lang. Treemaker 4.0: A program for origami design, 1998. http://www.langorigami.com.

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cover image ACM Conferences
SoCG '12: Proceedings of the twenty-eighth annual symposium on Computational geometry
June 2012
436 pages
ISBN:9781450312998
DOI:10.1145/2261250

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 17 June 2012

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Author Tags

  1. computational origami
  2. origami design
  3. rigidity
  4. treemaker
  5. universal molecule

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SoCG '12
SoCG '12: Symposium on Computational Geometry 2012
June 17 - 20, 2012
North Carolina, Chapel Hill, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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