Smooth Approximation to Surface Meshes of Arbitrary Topology with Locally Blended Radial Basis Functions

In this paper, we present a new approach for smooth approximation of surface meshes with arbitrary topology and geometry. The approach is based on the well-known radial basis functions (RBFs) for local shape approximation combined with a blending operator and a family of normalized weight functions for global surface construction. Our method first defines a local approximation using locally supported RBF for every vertex of the input mesh. A single global smooth surface is then constructed by blending the local approximations using weight functions associated with mesh vertices. A projection procedure is employed for visualizing the global surface using the local parameterization defined by barycentric coordinates for each facet of the input mesh. The approach provides a robust and efficient solution for smooth surface construction from various 3D mesh models.