Universal Hinge Patterns

We investigate a new approach to origami design using simple universal hinge patterns where the crease patterns for different shapes are just different subsets of a common hinge pattern. Several algorithms have previously been developed to design folded states for particular shapes, but they require a different crease pattern for each shape. Our motivations include the development of robotic "origami transformers, " artistic tools, and theoretical insights. We show how to compose "cube gadgets " to fold any N-cube polycube from an O(N) x O(N) rectangle of paper, using only O(N 2) time to compute the parameters of the unambiguous folding sequence. We also describe extensions of our basic algorithm to larger classes of shapes with improved paper efficiency. Finally, we demonstrate that an implementation of this technique can actually be used to partially automate geometric paper folding