Fig. 2: Optimization and automated generation of crease patterns.

a Optimization domain definition in terms of vertices and their dependencies. b Crease pattern graph and folded configuration of a simple origami before and after optimization. The goal of the optimization problem is to place the mobile vertices such that the target vertex reaches the target point in the folded configuration. c Pattern that was optimized sequentially to match the shape of an elephant in its folded configuration. Crease pattern graph defined in terms of unit cells before (grey) and after (black) optimization. d Sample crease pattern graph with folded configuration before and after expansion. The goal of the expansion is to reach the point marked in red. e Crease pattern graph and folded configuration of corresponding crease pattern that was subsequently extended to approach the shape of the seam on a tennis ball in the folded configuration. The crease pattern graph is shown using the vertex locations in the deformed configuration (the graph is shown as seen from the top view). Auxiliary vertices are shown in this graph.