Methods for anchoring boundary nodes when smoothing a triangular surface mesh

In numerical modeling tasks that use surface meshes, remeshing is often required. However, while remeshing, distortion can occur. The accumulation of distortions can lead to the collapse of the solution. Smoothing algorithms are used to maintain the quality of the mesh during the calculation. When performing smoothing using methods that shift the mesh nodes, the border nodes are usually fixed to avoid distortion. However, simply fixing the nodes can lead to more severe distortion. This paper presents methods for working with boundary nodes to control such nodes during the smoothing process. Algorithms for working with pseudo-3D surface meshes, which are of particular interest, are also considered.

Methods for anchoring boundary nodes when smoothing a triangular surface mesh

В задачах численного моделирования, использующих поверхностные сетки, часто требуется перестроение сетки. Однако при перестроении сетки могут возникать искажения. Накопление искажений может привести к развалу решения. Для того, чтобы поддерживать качество сетки в процессе расчета, применяются алгоритмы сглаживания. При выполнении сглаживания методами, сдвигающими узлы сетки, граничные узлы обычно закрепляют, чтобы избежать искажений. Однако простое закрепление узлов может привести к более серьезным искажениям. В данной работе предлагаются методы работы с граничными узлами, позволяющие контролировать такие узлы в процессе сглаживания. Также рассмотрены алгоритмы для работы с псевдотрехмерными поверхностными сетками, представляющими отдельный интерес.

Finite triangular surface mesh simplification with geometrical feature recognition

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.

Surface Mesh Normals Filter

We have previously developed a new surface mesh data structure in itk (~). In this document we describe a new filter () to estimate normals for a given triangular surface mesh in this data structure. Here we describe the implementation and use of this filter for calculating normals of a .