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Geodesic-Controlled Developable Surfaces for Modeling Paper Bending

We present a novel and effective method for modeling paper bending in interactive and animation applications. The method exploits the representation of a developable surface as the envelope of rectifying planes of a curve in 3D, which is therefore necessarily a geodesic on the surface. We manipulate the geodesic to provide intuitive shape control for modeling paper bending. Our method ensures a natural continuous isometric deformation from a piece of bent paper to its flat state without any size-stretching. Test examples show that the new scheme is fast, accurate, and easy to use, thus providing an effective approach to interactive paper bending. We also present extensions to handle paper of non-convex shape or composed of piecewise smooth developable surfaces.