The quantity and quality of the mesh elements are both significant factors for guaranteeing computational precision in the finite-element method (FEM). In most mesh simplification algorithms, the geometric error was thought to be the most important issue. However, the mesh quality was rarely taken into consideration. In this article, a finite triangular surface mesh simplification algorithm is proposed, in which the vertex dispersion is introduced to represent the local geometrical feature, and then either edge collapse or face collapse is carried out consequently. The aspect of the newly created face is taken into account and the position of the newly created vertex is obtained by solving an over-determined system of linear equations with respect to the aspect ratios of the newly created faces; thereupon the simplified mesh quality is improved. To obtain a further simplification and to reduce the errors in the succeeding FEM analysis, surface fitting is adopted on the surfaces with large curvature. Simplification cases had been performed in comparison with the quadric error metric method, and the results show that the definition of the local mesh density is more reasonable for the FEM analysis with the same simplification ratio while the present simplification algorithm is employed. Moreover, the mesh quality can be greatly improved on the surface with large curvature. A set of FEM numerical experiments of polymer injection moulding simulation had also been performed to determine the effect of the presented simplification algorithm on the FEM analysis. The numerical results show that the error of the injection pressure can be limited within 4 per cent, while the simplification percentage reaches 75 per cent.
A case study: impact of target surface mesh size and mesh quality on volume-to-surface registration performance in hepatic soft tissue navigation
