Remeshing by Curvature Driven Diffusion

Abstract

We present a method to regularize an arbitrary topology mesh M, which defines a piecewise linear approximation of a surface $\mathcal{M}$, with the purpose of having an accurate representation of $\mathcal{M}$: the density of the nodes should correlate with the regularity of $\mathcal{M}$. We use the mean curvature as an intrinsic measure of regularity. Unlike sophisticated parameterization-dependent techniques, our parameterization-free method directly redistributes the vertices on the surface mesh to obtain a good quality sampling with edges on element stars approximately of the same size, and areas proportional to the curvature surface features. First, an appropriate area distribution function is computed by solving a partial differential equation (PDE) model on the surface mesh, using discrete differential geometry operators suitably weighted to preserve surface curvatures. Then, an iterative relaxation scheme incrementally redistributes the vertices according to the computed area distribution, to adapt the size of the elements to the underlying surface features, while obtaining a good mesh quality. Several examples demonstrate that the proposed approach is simple, efficient and gives very desirable results especially for curved surface models with sharp creases and corners.