中文摘要：

借鉴刚架结构在力的作用下的变形原理，将线弹性有限元方法应用于网格的变形设计中，结合骨架驱动生物运动的机制和线弹性有限元方法，提出一种运用形函数插值计算网格变形的造型算法．首先通过创建几何模型的低分辨率骨架建立有限元刚架模型，并计算网格模型顶点与梁单元自然坐标间的映射；然后交互地添加边界条件（如固支或铰支）、施加外部载荷（如集中力或力偶）计算刚架的节点位移；最终根据梁单元的形函数插值节点位移得到初始网格模型顶点变形后的新位置．该算法针对几何模型的大变形问题，运用旋转场修正方式避免了大变形的失真；此外，在节点两侧的挠度曲线间构造了C1连续的3次Hermite插值曲线，消除了旋转场修正中的褶皱和纽结现象，实现了网格模型的光滑变形．实验结果表明，该算法可高效地实现伸缩、弯曲、旋转等变形操作．

英文摘要：

Using the deformation principle of rigid frame under force for reference, linear elastic FEM is applied to realize deformation design of mesh model. Combining skeleton-driven biological motion with linear elastic FEM, an efficient deformation algorithm is proposed based on finite element shape function interpolating. Firstly, the rigid frame is constructed by building low-solution skeleton of the original mesh. Secondly, the map between mesh vertices and beam is established to realize skeleton- driven mesh deformation. Thirdly, through adding boundary conditions and exerting external load interactively, node displacement could be calculated by solving global stiffness matrix equation. I.astly, displacement vector of mesh vertices are computed out by interpolating node displacements with shape function. （）wing to the limitation of linear FEM in large deformation problem, a rotating field is established to modify this drawback and the cubic Hermite interpolation is introduced to interpolate two ends of deflection curves at common node to realize smooth deformation results. Experimental results show this algorithm is effective and can be applied to model deformation such as expanding, bending, rotating and other operations.