Volume Conservation of 3D Surface Triangular Mesh Smoothing

Daniel Rypl, Jiří Nerad

Department of Mechanics
Faculty of Civil Engineering
Czech Technical University in Prague
Thákurova 7, 166 29 Prague, Czech Republic


Present paper deals with a shrinkage free smoothing of triangular isotropic meshes over three-dimensional surfaces. Adopted approach is based on Laplacian smoothing combining in 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 noise, the weights are derived in a very simple way using a "do-not-harm" concept. The paper also extends the application of the smoothing from closed surfaces to open surfaces and their combination. The performance and capabilities of the presented methodology are demonstrated on several examples.