Non-Parametric Conserving Smoothing Method of Area, Volume and Mass for Piecewise Linear Curves and Surfaces

Abstract

The interest in curve/surface smoothing has increased in many fields, such as computer graphics and computational fluid mechanics, due to it’s various applications in these fields. Different approaches have been used to smooth surfaces such as Laplacian approach which is a very popular approach. However, in many simulations, area, volume, mass and sometimes shape have to be preserved. In this work, we present several nonparametric smoothing algorithms which preserve area, volume and mass of curve or surface grids depending on Laplacian algorithm. A new application of area conserving smoothing method of planar polygonal regions in the space will be presented.