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Geometry of axisymmetric 3D origami consisting of triangular facets. (English) Zbl 1383.51037

Summary: 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.

MSC:

51M15 Geometric constructions in real or complex geometry
51N20 Euclidean analytic geometry
52B70 Polyhedral manifolds
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References:

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