A Novel Surface Remeshing Scheme via Radial Basis Functions and Higher-Dimensional Embedding

Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. The quality of the meshes directly impacts numerical simulations. In practice, however, one often has to deal with several challenges to construct suitable meshes. Some regions in a naively built mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel surface remeshing procedure which greatly improves a problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher-dimensional embedding surface remeshing technique, we can automatically generate a new anisotropic surface mesh with improved mesh quality. Moreover, we are not only able to refine or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy