Mesh and CAD repair based on parametrizations with radial basis functions

Abstract

The goal of this paper is to present a new repair process that includes both model/mesh repair and mesh generation. The repair algorithm is based on an initial mesh of the CAD that may contain topological and geometrical errors. This initial mesh is then remeshed by computing a discrete parametrization with radial basis functions (RBF's). [34] showed that a discrete parametrization can be computed by solving PDE's on an initial correct triangulation using finite elements. Paradoxically, the meshless character of the RBF's makes it an attractive numerical method for solving the PDE's for the parametrization in the case where the initial mesh contains errors. In this work, we implement the Orthogonal Gradients method which was recently introduced in [32], as a technique to solve PDE's on arbitrary surfaces with RBF's. We will implement the low order version of the algorithm, which already gives great results in this context. Different examples show that the presented method is able to deal with errors such as gaps, overlaps, T-joints and simple holes and that the resulting meshes are of high quality. Moreover, the presented algorithm can be used as a hole-filling algorithm to repair meshes with undesirable holes. The overall procedure is implemented in the open-source mesh generator Gmsh [18].