Geometric fairing of irregular meshes for free-form surface design

In this paper we present a new algorithm for smoothing arbitrary triangle m eshes while satisfying G(1) boundary conditions. The algorithm is based on solving a nonlinear fourth order partial differential equation (PDE) that o nly depends on intrinsic surface properties instead of being derived from a particular surface parameterization. This continuous PDE has a (representa tion-independent) well-defined solution which we approximate by our triangl e mesh. Hence. changing the mesh complexity (refinement) or the mesh connec tivity (remeshing) leads to just another discretization of the same smooth surface and doesnt affect the resulting geometric shape beyond this. This i s typically not true for filter-based mesh smoothing algorithms. To simplif y the computation we factorize the fourth order PDE into a set of two neste d second order problems thus avoiding the estimation of higher order deriva tives. Further acceleration is achieved by applying multigrid techniques on a fine-to-coarse hierarchical mesh representation. (C) 2001 Elsevier Scien ce B.V. All rights reserved.