基于能量极小准则的曲面再现与光顺

Reconstruction and Smoothing of Surface Based on Minimum Energy Principle

根据能量最小原理及数据逼近理论 ,提出一种基于散乱数据重建光顺自由曲面的方法 .该方法采用 Her-m ite单元极小化目标泛函 ,再现的曲面全场 C1或 C2连续 .这种结合能量光顺的有限元方法抑制了输入数据中噪声的影响 ,可给出曲面一阶导数甚至二阶导数 .讨论光顺因子对计算精度的影响 。

Uniform rectangular meshes are constructed to cover all given scattered points. Energy functional of thin plate represented as Hermite surface patches with C 1 or C 2 continuity throughout the whole data field is minimized to fit the data points. Such an approach of global optimization is very effective to suppress the influence of noise in input data and reliable derivatives of first order even second order can be calculated. Effects of smoothing parameter on the precision of surface reconstruction are investigated and the applicability of presented method is illustrated by two practical examples.