C1连续曲面重构与光顺的有限元算法

提出了一种基于离散的测量数据重建光顺自由曲面的有限元新方法。根据最佳逼近与能量光顺原理，建立正定的目标泛函，采用18自由度三角形板单元对泛函离散，进行极小化，求得最优解。根据有限元插值计算，重新构造出全场C^1连续的自由曲面。这种方法结合了能量光顺技术，有效地抑制了输入数据上误差噪声的影响，曲面重建的精度高、光顺性好，而且能给出合理的一阶导数。该方法计算简单、便于应用，所需的输入数据点少，并可用于处理曲线边界区域的问题。

Finite Element Algorithm for C1 Surface Reconstruction and Smoothing

A new finite element algorithm for the reconstruction and smoothing of freeform surface from the discrete measured data is presented in the paper. Based on the theory of optimal approximation and energy smoothing principle, a positive definite functional is constructed and minimized by use of 18 degree-of-freedom triangular plate bending element, thereby the optimal solution is obtained and C1 freeform surface is reconstructed by finite element interpolation. The influence of noise in measured data is eliminated effectively since the method is combined with smoothing technique. The surface reconstructed is of high approximating precision and good smoothness, and reliable derivatives of first order can be calculated by FEM. This method is easy and expedient to use. The number of input data required in the presented method is less than that in numerical interpolation and fitting. The method can be used to the problem of irregular region with curved boundary.