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.


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