Lang's Universal molecule algorithm

8 years 9 days ago

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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 site1 . 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. Categories and Subject Descriptors I.3.5 [Computational Geometry and Object Modeling]: [Geometric algorithms, languages, and systems] General Terms Theory, Algorithms Keywords computational origami, Universal Molecule, TreeMaker

John Christopher Bowers, Ileana Streinu

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