保特征的加权最小二乘三角网格光顺算法

Feature-preserving Mesh Smoothing Algorithm Based on the Weighted Least Squares

在逆向工程和计算机图形学中,由扫描得到的数据多存在噪声,为了对其进行光顺处理,提出一种基于加权最小二乘思想的保特征网格光顺算法.首先提出一个关于光顺后网格顶点或者法向的离散二次能量函数,该能量一方面满足光顺后的网格在除特征点外的地方处处光滑的同时,还满足光顺后网格与原噪声网格尽可能相似;然后对此能量函数关于每个顶点求偏导数并使其为0,得到一个线性方程组,求解该方程组得到光顺后的网格.实验结果表明,该算法是线性的,复杂度低,且无需人工交互就可以很好地保持网格的尖锐特征,还能避免发生收缩现象.

Mesh smoothing is often required in the inverse engineering and computer graphics applications where the acquisition data are usually very noisy.In this paper we propose a feature-preserving mesh smoothing algorithm based on the weighted least squares.A discrete quadratic energy related to the smoothed mesh vertices and normal is introduced which considers not only the overall smoothness of the mesh but also the preservation of the fine features of the original model.Then a quadratic objective function based on this energy is minimized by solving a sparse linear system to get the smoothed mesh.Experiments have shown that this linear,easy to implement algorithm can preserve sharp features without any user intervention,and can avoid shrinkages very well.