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abstract

Lang's universal molecule algorithm

Published:17 June 2012Publication 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.Google ScholarGoogle Scholar
  2. J. C. Bowers and I. Streinu. Rigidity of Lang's origami universal molecules. Technical report, Feb 2012. (Submitted).Google ScholarGoogle Scholar
  3. R. J. Lang. Origami design secrets: mathematical methods for an ancient art, A. K. Peters, 2003.Google ScholarGoogle Scholar
  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. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. R. J. Lang. Treemaker 4.0: A program for origami design, 1998. http://www.langorigami.com.Google ScholarGoogle Scholar

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  1. Lang's universal molecule algorithm

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      • Published in

        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

        Copyright © 2012 Authors

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        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 17 June 2012

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        Overall Acceptance Rate625of1,685submissions,37%

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