Multi-strip smooth developable surfaces from sparse design curves

Abstract Creating developable surfaces from sparse design curves finds important applications in industrial design and modeling. Existing methods aim at finding a quasi-developable surface with as large developability as possible to interpolate design curves. Even so, the fabrication of industrial products with inextensible materials puts a higher request for surface developability. We propose a method to explore the space of developable surfaces whose boundaries are restricted in the close neighborhood of input design curves and aim at obtaining a smooth surface of a high degree of developability bounded by smooth curves perturbed from input curves. This is achieved by computing a developable surface with approximate boundaries, which is obtained by solving a geometric optimization problem. The performance of the proposed method is demonstrated by a number of experiments of design and fabrication of some industrial products with paper.