A unified approach for fairing arbitrary polygonal meshes

Abstract

Arbitrary polygonal meshes play an important role in 3D model representation and surface modeling. Most of the previous smoothing approaches are, however, mainly designed for triangular meshes. This paper proposes a unified approach to address fairing problems of arbitrary polygonal meshes. The approach is built upon an assumption that all face centroids of a smoothed mesh locate on its noise-free surface and remain unchanged during the smoothing process in order to prevent the resulted mesh from shrinkage and preserve surface features. Boundary smoothing is considered in a similar way as well but the process is independent to mesh processing such that two noisy meshes sharing a boundary still adjoin continuously after smoothing. Finally, a Taubin-like inflation operator is employed to further improve the ability of anti-shrinkage. Although very simple iterative equation is employed in the smoothing procedure, experiments demonstrate that the approach is able to not only effectively address the problem of shrinkage and distortion but also preserve features very well.