Volume Preserving Smoothing of
Triangular Isotropic Three-dimensional Surface Meshes
Daniel Rypl, Jiří Nerad
Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic
Abstract:
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.