Ruling Based Design Method of Curved Origami

Curved origami attracts the attention of designers in recent years for the potential in the field of building structures for free form curved design. For practical use, the design methods are required to link the mathematically obtained curved surface and the requirements of architectural functions. Therefore, in this paper, we propose a method to solve the shape determination problem from predefined developable surfaces described by initial rulings. The initial rulings can be conical or cylindrical surfaces. By means of inputting the ruling lengths, the 3D configuration of the origami model can be obtained. To decrease the number of unknowns, the ruling lengths are mapped by control points of Non-Uniform Rational B-Spline (NURBS) techniques. The numerical example demonstrates the feasibility of finding curved origami with both dome-like and saddle-shaped surfaces and tubular models. This research focuses on the application to architectural engineering, aiming to determine the shape of curved origami using bending deformation to explore the possibility of applying curved origami to building structures.