We solve the task of representing free forms by an arrangement of panels that are manufacturable by precise isometric bending of surfaces made from a small number of molds. In fact we manage to solve the paneling task with surfaces of constant Gaussian curvature alone. This includes the case of developable surfaces which exhibit zero curvature. Our computations are based on an existing discrete model of isometric mappings between surfaces which for this occasion has been refined to obtain higher numerical accuracy. Further topics are interesting connections of the paneling problem with the geometry of Killing vector fields, designing and actuating isometries, curved folding in the double-curved case, and quad meshes with rigid faces that are nevertheless flexible.
Bibliographical noteKAUST Repository Item: Exported on 2021-05-04
Acknowledgements: This work was supported by the Austrian Science Fund via grants I2978 (SFB-Transregio programme Discretization in geometry and
dynamics), W1230 (DK programme Discrete Mathematics) and F77 (SFB grant Advanced Computational Design). V. Ceballos, C. Jiang,
F. Rist, and H. Wang were supported by KAUST baseline funding.