《Geodesic-Controlled Developable Surfaces for Modeling Paper Bending》.pdf

EUROGRAPHICS 2007 / D. Cohen-Or and P. Slavík Volume 26 (2007), Number 3 (Guest Editors) Geodesic-Controlled Developable Surfaces for Modeling Paper Bending Pengbo Bo and Wenping Wang The University of Hong Kong Abstract We present a novel and effective method for modeling a developable surface to simulate paper bending in interac- tive 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 continu- ous isometric deformation from a piece of bent paper to its flat state without any 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 show how to handle non-convex piecewise smooth developable surfaces. Categories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism 1. Introduction state, i.e., stretching or shrinking of the paper size is not allowed. Paper is commonly used material. Therefore its shape mod- eling and animation is of great interest to computer graph- The last requirement means that there is an isometric map- ics. We are interested in inte