中文摘要：

为解决传统网格自由变形（FFD）结果往往不自然的问题,提出一种基于调和函数的变形算法.基于三维网格模型的拓扑信息,采用离散化的Laplace-Beltrami算子计算物体表面的调和函数,并以之引导物体进行自然形变.实验结果表明,借助于调和函数具有的光滑性和稳定性特点,该算法能够通过简洁的操作实现三维模型的自然变形,不仅克服了传统FFD算法的局限性,并且可以支持句柄操作的动态调整,具有良好的交互性.

英文摘要：

Based on Laplace operator,a harmonic field deformation algorithm is proposed in this paper.The proposed method manipulates the control handles to achieve a natural deformation that could not be reproduced by traditional free-form deformation（FFD） algorithms.Different from the existing FFD algorithms,the proposed free-form deformation method is based on topology information,using a discretized Laplace-Beltrami operator to compute the harmonic field of the mesh,which in turn can produce a natural deformation of the guided objects.Experiments show that using simple operations of the natural deformation of 3D meshes,the proposed algorithm not only overcomes the inherent limitations in traditional FFD methods,but also can support dynamic adjustment of control handles with real-time performance.