中文摘要：

针对复杂三角网格的网格参数化问题提出了一种基于线弹性反向变形有限元法的网格参数化方法。为了能够减少三角网格参数化带来的网格扭曲，首先采用保持网格伸缩内在量的方法将空间网格展平；然后以上述展平网格作为初始迭代解，建立线弹性有限元方法迭代方程，通过迭代求解使的网格节点残余内力或节点位移满足事先给定的收敛条件，最终求得网格参数化结果。计算结果表明，该方法能得到较好的参数化结果，非常适于复杂曲面的网格重划分等计算机辅助设计的应用。

英文摘要：

We use the finite element method for linear-elastic reverse deformation to parameterize a complex triangle nesh. To reduce the distortion caused by triangle mesh parameterization, we apply the mesh＇s intrinsic flexibility naintenance method to flattening the 3D mesh and then take the flattened mesh as the initial iterative mesh to estab- lish the iterative equation with the finite element method for linear-elastic reverse deformation. Through the iterative solution, we obtain the mesh parameterization results that can make the residual internal force of a mesh node or the node displacement satisfy the convergence conditions. The calculation results show that our method can obtain bet- ter parameterization results and is very suitable for computer aided design applications such as re-dividing the me- shes of a complex surface.