Homogeneous deformation following the shape of a parametric surface

Free-form deformation through the control of parametric surfaces is a flexible technique. With the old method objects to be deformed are embedded into the parametric space of the base surface directly and the undesired distortions are frequently introduced into the result. A homogeneous deformation method is proposed which successfully eliminates or alleviates the undesired distortion. The main difference between the proposed method and the existing methods is that the new one embeds objects into the parametric space of the base surface by isometric or locally isometric mapping using the planar development of the base surface as the intermediate medium, thus the object to be deformed can follow the shape of the base surface homogeneously. Implementation results indicate the potentials of the new approach.