Compact Folding of Thick Origami via Stacking

Recent techniques enable folding planer sheets to create complex 3D shapes, however, even a small 3D shape can have large 2D unfoldings. The huge dimension of the flattened structure makes fabrication difficult. In this paper, we propose a novel approach for folding a single thick strip into two target shapes: folded 3D shape and stacked shape. The folded shape is an approximation of a complex 3D shape provided by the user. The provided 3D shape may be too large to be fabricated (e.g. 3D-printed) due to limited workspace. Meanwhile, the stacked shape could be the compactest form of the 3D shape which makes its fabrication possible. The compactness of the stacked state also makes packing and transportation easier. The key technical contribution of this work is an efficient method for finding strips for quadrilateral meshes without refinement. We demonstrate our results using both simulation and fabricated models.