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

Authors:
Abel Gargallo-Peiró;Xevi Roca;Josep Sarrate
Affiliations:
Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain 08034;Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, USA 02139;Laboratori de Càlcul Numèric (LaCàN), Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya, Barcelona, Spain 08034
Venue:
Computational Mechanics
Year:
2014

Citing 6
Cited 0

Algebraic Mesh Quality Metrics

SIAM Journal on Scientific Computing
Algebraic mesh quality metrics for unstructured initial meshes

Finite Elements in Analysis and Design
Isotropic Surface Remeshing

SMI '03 Proceedings of the Shape Modeling International 2003
Non-iterative approach for global mesh optimization

Computer-Aided Design
Simultaneous aligning and smoothing of surface triangulations

Engineering with Computers - Special Issue: 17th International Meshing Roundtable - 2008; Guest Editor: Rao V. Garimella
Simple and effective variational optimization of surface and volume triangulations

Engineering with Computers - Special Issue: 17th International Meshing Roundtable - 2008; Guest Editor: Rao V. Garimella

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.