Deforming Developable Surfaces

One of the techniques in digital geometry processing that has been studied for many years is mesh deformation. Recently, researchers have proposed deformation methods that preserve certain aspects of the mesh, such as geometric features and material properties. In this project we look at preserving developability of a surface. Specifically, if it is known that a surface is developable before deformation, it would be desirable to maintain developability during and after the deformation. To this end, a new technique for deforming surfaces is developed by manipulating the Gauss map of the surface. This technique can be considered a variation of gradient deformation, with additional constraints that account for Gaussian curvature. Finally, a simple method for deformation transfer using this framework is described, which does not rely on any parameterization between the models.