A Method for Designing Flat-Foldable 3D Polygonal Models

Abstract

We propose a method for designing targeted 3D polygonal models that can be folded flat, which consist of side panels as well as horizontal top and bottom panels. Vertically adjacent panels are connected by hinges at their horizontal edges. The models can be folded flat by pushing down the top panel, while they can be also deployed by pulling up the top panel. The key idea in making the model so that it can be folded flat is to add vertical slits along the edges of side panels; the horizontally adjacent side panels are separated in the folded state, and are connected to form a closed solid model in the deployed state. Our method takes the shapes of the top panel as well as the cross sections of the side panels as inputs. Users of our prototype system first simply draw the top panel as a convex polygon. They then draw polylines to specify the cross sections. Since the polyhedral model generated by the input data rarely satisfies flat-foldability conditions, our system modifies the positions of the vertices in cross sections based on numerical optimization. Unlike most origami design systems that ignore material thickness, our system can output the 3D geometry of panels so that they can be used to form a closed 3D model with a certain thickness.