关键词: 曲面折展, 可展曲面, 高斯映射, 曲面离散, 曲率

Abstract: Gauss map of the continuous curved surfaces is lent to model the geometry properties and configuration information of spatial curved origami. The Gauss spherical curves achieve the goal of dimension deduction of the discretization problem in which R³ surface discretization is shifted to spherical curve discretization. Then, the equal segments are utilized to discretize the spherical curves first. The resulting points on the spherical curves present the discretized normal directions of the curved surface. Thus, the discretized ruling lines, as new folds in the approximate polyhedron, can be obtained. The aim of this work has been to provide a curvature discretization for developable surfaces based on the Gauss spherical curves. The directed foldable units are identified and the discrete operations of these units are proposed. More complex curved origami can be analyzed with its decomposition and the constructive units. It provides a differential geometry means to deal with the instantaneous folding movements. Folding with non-flat curvature is exploited. The equal curvature discretization of curved surface is realized.

Key words: curved origami, developable surface, Gauss map, curved discretization, curvature