Curved Crease Origami

Most origami, both practical and mathematical, uses just straight creases. Curved creases, on the other hand, offer a wealth of new design possibilities. While the first curved-crease models date back to the Bauhaus in the 1930s, curved creasing remains relatively underexplored. The principal challenge considered here is to understand what 3D forms result as natural resting state(s) after folding a set of curved creases, with the potential to enable a new category of design. This problem goes beyond the mathematics of developable surfaces to a question of physics: equilibria of an unstretchable surface with uncreased and creased (plastically deformed) portions folding elastically toward desired angles. Two natural approaches for experimenting with this question are computer simulation and building real models. We follow the latter approach, being more interested in how real materials behave and how the resulting structures might be applied in the field of architecture.