Multi-strip smooth developable surfaces from sparse design curves. (September 2019) - Bo, Pengbo; Zheng, Yujian; Jia, Xiaohong; Zhang, Caiming
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. Highlights: We propose a method to create seamless multi-strip smooth developable surfaces from an array of design curves. We achieve high accuracy of developability with the controllable error in curve modification. Original curves are modified and extended automatically when necessary which is driven by the surface developability.