A surface mesh smoothing and untangling method independent of the CAD parameterization

作者：Gargallo Peiro Abel; Roca Xevi; Sarrate Josep^*

来源：Computational Mechanics, 2014, 53(4): 587-609.

DOI：10.1007/s00466-013-0920-1

• Mesh quality
• Mesh optimization
• Smoothing and untangling
• CAD surfaces

A method to optimize triangular and quadrilateral meshes on parameterized surfaces is proposed. The optimization procedure relocates the nodes on the surface to improve the quality (smooth) and ensures that the elements are not inverted (untangle). We detail how to express any measure for planar elements in terms of the parametric coordinates of the nodes. The extended measures can be used to check the quality and validity of a surface mesh. Then, we detail how to optimize any Jacobian-based distortion measure to obtain smoothed and untangled meshes with the nodes on the surface. We prove that this method is independent of the surface parameterization. Thus, it can optimize meshes on CAD surfaces defined by low-quality parameterizations. The examples show that the method can optimize meshes composed by a large number of inverted elements. Finally, the method can be extended to obtain high-order meshes with the nodes on the CAD surfaces.

• 出版日期2014-4