A Method for Designing Crease Patterns for Flat-Foldable Origami with Numerical Optimization

Origami is the art and science of making various shapes by simply folding a sheet of paper. When origami is studied as a geometrical problem, it is often assumed that the origami is folded flat. This flat foldability is an important property when we consider applying the techniques of origami to increase the portability and storage space of industrial products. We propose a method to generate new crease patterns that are flat-foldable by using a computer with the algorithm of numerical optimization. In this paper, we describe the five steps of our method. Although the numerical optimization sometimes fails to converge and we have to go back to the first step, we can generate many flat-foldable crease patterns containing randomly placed vertices. Our method can generate patterns that can be used not only as new origami designs but also as problems for the origami puzzle “Fold Me Up”.