散乱分布数据曲面重构的光顺-有限元方法

提出了一种基于散乱分布的数据点重构三维曲面的有限元方法.根据最佳逼近与数据光顺理论建立正定的目标泛函,采用有限元最佳拟合使泛函极小化,求得最优解.通过八节点等参数有限元插值计算,重新构造出三维曲面.这种光顺-有限元方法有效地抑制了输入数据上误差噪声的影响,与有限元拟合方法相比,所需的输入数据点少,重构的曲面逼近精度高、光顺性好.数值实验表明,该方法简单,便于应用.

A Smoothing-Finite Element Method for Surface Reconstruction from Arbitrary Scattered Data

A finite element method to reconstruct 3D surface from the scattered data is presented in the paper. Based on the theories of optimal approximation and data smoothing, a positive definite functional is constructed and minimized by using the finite element best-fitting technique, then the optimal solution is obtained and the 3D surface is reconstruct by eight-node isoparametric finite element interpolation. The influence of noise in input data is eliminated effectively by the smoothing-finite element method. The number of input data required in the presented method is less than that in finite element fitting. The surface reconstructed is of high approximating precision and good smoothness. Numerical results show that this method is simple and expedient to use.