Folding Rigid Origami With Closure Constraints

Rigid origami is a class of origami whose entire surface remains rigid during folding except at crease lines. Rigid origami finds applications in manufacturing and packaging, such as map folding and solar panel packing. Advances in material science and robotics engineering also enable the realization of self-folding rigid origami and have fueled the interests in computational origami, in particular the issues of foldability, i.e., finding folding steps from a flat sheet of crease patterns to desired folded state. For example, recent computational methods allow rapid simulation of folding process of certain rigid origamis. However, these methods can fail even when the input crease pattern is extremely simple. This paper attempts to address this problem by modeling rigid origami as a kinematic system with closure constraints and solve the foldability problem through a randomized method. Our experimental results show that the proposed method successfully fold several types of rigid origamis that the existing methods fail to fold.