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Journal for Geometry and Graphics 21 (2017), No. 1, 107--118
Copyright Heldermann Verlag 2017



Geometry of Axisymmetric 3D Origami Consisting of Triangular Facets

Yan Zhao
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
yanzhao.npal.tsukuba@gmail.com

Yoshihiro Kanamori
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
kanamori@cs.tsukuba.ac.jp

Jun Mitani
Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
mitani@cs.tsukuba.ac.jp



We propose a novel design method for 3D origami consisting of triangular facets with an axisymmetric structure. Our method interactively designs a rotationally-symmetric crease pattern and then analytically calculates the 3D origami with real-time human interaction. The proposed method enables us to change one parameter to axisymmetrically deform the 3D origami while preserving its developability. By changing another parameter, our method leads to a way of folding a 3D origami called "along-arc flat-folding". By using our prototype system, we interactively explore various origami designs before actually making them. Several 3D origami pieces and folding sequences are presented to demonstrate the validity.

Keywords: Computational origami, axisymmetric, deployable structure, flat-foldable.

MSC: 51N20; 52B70

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