沿参数曲面的均匀变形方法

基于参数曲面控制的物体自由变形是一项实用的技术，在已有的方法中，待变形物体被直接主控制曲面的参数空间，由于映射的非线性，导致物体变形同扭曲现象，本提出了一种基于参数曲面控制的均匀变形方法，新方法中，变形控制曲面首先以等距或局部等怕方式展开为平面，然后经由平面的线性映射，将待为形物体嵌入控制曲面的参数空间中，从而产生符合控制曲面形状的局部均匀变形，实验结果表明，本方法所产生的结果是令人满意的。

Homogeneous Deformation Following the Shape of a Parametric Surface

Free form deformation through the control of parametric surfaces is a flexible technique. In 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 in this paper 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.