3D Model Deformation via Conformal Mapping

In this paper, we introduce conformal mapping to 3D model deformation. The surface of the solid model is represented by base-patch and cross-section function. Accordingly, the shape of the 3D model can be modified by interactive means, such as changing the corresponding base-patch with conformal mapping and adjusting a cross-section function. There are two features of the proposed method. First, due to the properties of conformal mapping, the scheme satisfies the local demands on rigidity and still allows for considerable global deformation. Second, the deformation effect is predictable and the transformation function of the deformation can be expressed analytically. The proposed transformation of 3D deformation is continuous, not self- intersection, and topologically consistent. Some examples are presented in the end of the paper to illustrate the efficiency of our approach.