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

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.