A weighted mean approach to smooth parametric representation of polygon meshes

A method for representing genus-zero polygon meshes by smooth parametric surfaces is described. A surface is defined by a weighted sum of linear functions, each describing a polygon face in parametric form. Rational Gaussian blending functions that adapt to the size and shape of mesh faces are used as the weights. The proposed representation has a very high degree of continuity everywhere and provides a smoothness parameter that can be varied to produce surfaces at varying resolutions. It is shown that the representation facilitates geometry processing of meshes. The use of locally supported weight functions as an alternative to rational Gaussian weights is also discussed.