Flat-Foldable Axisymmetric Structures with Open Edges
Details
We propose a method to design axisymmetric structures that can be folded flat. The flat configuration of the model is obtained by pushing the structure downwards. Our model is represented by a polyhedron with a vertical symmetry axis. The edges that are not coplanar to the axis are hinges that connect two faces allowing their dihedral angle to change. The other edges are open during the folding process, binding two faces only in the original 3D configuration. The design interface consists in using mouse clicks to input an arbitrary outline formed by connected line segments. This outline is the desired axial cross section of the model. Usually, the input produces structures that are not flat-foldable and, therefore, we have to adjust the length and position of the line segments to enable flat-foldability. This is an optimization process, changing the outline the minimum possible. In this process, we consider the assignment of the fold directions on hinges in order to make the folding process easier. Finally, we output the data of a flat-foldable model, the assignment of fold directions and the animation of the folding process.
