A new triangular mesh repairing method using a mesh distortion energy minimization-based mesh flattening method. (May 2019) - Oh, Sahuck
Highlights: A new triangular mesh repairing method is proposed in the paper. A 3D mesh is mapped to a 2D parametric space by solving harmonic equations. Mesh points in the parametric space are repositioned to minimize the distortion of triangles. Mesh repairing is performed in the distortion-minimized planar mesh. Quality of incomplete meshes that have defects can be improved by the proposed method. Abstract: In this paper, we present a new method of repairing triangular meshes that have defects such as holes, mesh gaps, mesh overlaps, and T-junctions. The new method in this paper connects the open vertices arising from mesh errors using the Delaunay triangulation, and maps the connected mesh into the parametric planar space by solving harmonic equations. In a parametric space, the mesh points are moved to optimal positions where the distortion energy of the mesh caused by mesh flattening is minimized. The optimally positioned mesh is then repaired to improve its quality in the parametric space to create an isotropic mesh, and the quality-improved planar mesh is mapped back to the real space. The 3D mesh obtained from this procedure preserves good mesh characteristics in parametric space because the proposed method significantly minimizes triangular mesh distortion when the 3D mesh in the real space is mapped to the parametric space and vice versa. For this reason, compared with current parametric space based mesh repairing methods that require complicated work to compensate for the distortion between two meshes in the parametric space and real space, but can be problematic when an initial mesh has severe mesh errors, the proposed method can easily improve the quality of the mesh with high fidelity. Analytic and industrial incomplete meshes were repaired with the proposed methods, which show that the low quality of the incomplete meshes were significantly improved after applying the proposed method.