CAD and mesh repair with Radial Basis Functions
In this paper we present a process that includes both model/mesh repair and mesh generation. The repair algorithm is based on an initial mesh that may be either an initial mesh of a dirty CAD model or STL triangulation with many errors such as gaps, overlaps and T-junctions. This initial mesh is then remeshed by computing a discrete parametrization with Radial Basis Functions (RBFs). We showed in [1] that a discrete parametrization can be computed by solving Partial Differential Equations (PDEs) on an initial correct mesh using finite elements. Paradoxically, the meshless character of the RBFs makes it an attractive numerical method for solving the PDEs for the parametrization in the case where the initial mesh contains errors or holes. In this work, we implement the Orthogonal Gradients method to be described in [2], as a RBF solution method for solving PDEs on arbitrary surfaces. Different examples show that the presented method is able to deal with errors such as gaps, overlaps, T-junctions 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 [3].
radial basis functions rbf orthogonal gradients method geometry processing hole filling algorithm surface remeshing surface parametrization stl file format surface mapping harmonic map