Direct Resampling for Isotropic Surface Remeshing

Abstract

We present a feature-sensitive remeshing algorithm for relaxation-based methods. The first stage of the algorithm creates a new mesh from scratch by resampling the reference mesh with an exact vertex budget with either uniform or non-uniform vertex distribution according to a density function. The newly introduced samples on the mesh surface are triangulated directly in 3D by constructing a mutual tessellation. The second stage of the algorithm optimizes the positions of the mesh vertices by building a weighted centroidal Voronoi tessellation to obtain a precise isotropic placement of the samples. We achieve isotropy by employing Lloyd's relaxation method, but other relaxation schemes are applicable. The proposed algorithm handles diverse meshes of arbitrary genus and guarantees that the remeshed model has the same topology as the input mesh. The density function can be defined by the user or derived automatically from the estimated curvature at the mesh vertices. A subset of the mesh edges may be tagged as sharp features to preserve the characteristic appearance of technical models. The new method can be applied to large meshes and produces results faster than previously achievable.