Layered deformation of solid model using conformal mapping

In this paper, we present a solid model deformation method based on layered conformal mapping. For a solid model represented by base patch and height field, the shape of the model can be deformed by interactive means, such as changing the base patch by conformal mappings and adjusting the height field by a pre-defined function. In our method, the deformation is predictable and the transformation function of the deformation can be expressed analytically by Schwarz–Christoffel formula. To perform a deformation of a cylinder to a desired solid of rotation hierarchically, a generalized Schwarz–Christoffel formula is also introduced. Numerical examples show that the proposed method is convenient and efficient to deform solid models, especially to solids with genus zero.