Interactive Design of Planar Curved Folding by Reflection

Designing curved folds of a developable surface remains an open problem. No analytical method for the design of curved folds has been reported. Although optimization methods exist, it is difficult to interactively design valid curved folds of a single developable surface using such methods. In the present paper, we propose an interactive system for designing a surface with planar curved folds based on mirror reflection. The key consideration is that a surface created by sequential reflective folding is guaranteed to be isometrically unfolded into a plane. We demonstrate that the proposed system enables the interactive design of a variety of expressive curved folds, which was very difficult using previous methods.