Volume-controlled surface fairing

Abstract

Surface fairing is a central geometry processing tool, routinely used for denoising and smoothing applications---see [Botsch et al. 2006], Chap. 7 for an overview of the extensive literature on the subject. A notorious shortcoming of basic fairing schemes is volume shrinkage. Existing remedies often suffer from sensitivity to choice of parameters [Taubin 1995], are subject to unnatural global effects [Hermosillo et al. 1999], or resort to higher-order, computationally intensive surface evolutions [Bobenko and Schröder 2005]. Instead, we propose a simple, efficient and unconditionally stable smoothing scheme that implements a locally volume-controlled flow, with near preservation of volume. Our approach directly modifies the implicit fairing scheme [Desbrun et al. 1999], but it can be used to build volume control into any other surface flow.