Volume preserving smoothing of triangular isotropic three-dimensional surface meshes

The present paper deals with the volume preserving smoothing of triangular isotropic meshes over three-dimensional surfaces. The adopted approach is based on Laplacian smoothing combining in an alternating manner positive and negative weights in consecutive cycles of the smoothing. Since the aim is to improve the shape of individual elements of the mesh rather than to get rid of a noise, the weights are derived in a very simple way using a “do not harm” concept. The paper also extends the smoothing methodology from meshes on closed surfaces to meshes on open surfaces and discusses how the concept can be applied to meshes over surfaces with sharp features and curvature discontinuities. The performance and capabilities of the presented smoothing approach are demonstrated on several examples.