Surface deformation with differential geometric structures Original Research Article

This paper considers the deformation of a given surface to a surface that smoothly connects to previously designed surfaces while reflecting the overall shape of the initial surface. We introduce deformation energy using a Laplacian-based functional, which is defined by the global differential geometric structures of the initial surface. It is shown that the proposed deformation energy does not depend on representations of the initial surface, and relates to the mean curvature vector, a geometric quantity correlated to overall surface shape, and also has a good computational property. An example is presented to demonstrate the effectiveness of our method.