Automatic surface mesh generation for discrete models – A complete and automatic pipeline based on reparametrization

Abstract

Triangulations are an ubiquitous input for the finite element community. However, most raw triangulations obtained by imaging techniques are unsuitable as-is for finite element analysis. In this paper, we give a robust pipeline for handling those triangulations, based on the computation of a one-to-one parametrization for automatically selected patches of input triangles, which makes each patch amenable to remeshing by standard finite element meshing algorithms. Using only geometrical arguments, we prove that a discrete parametrization of a patch is one-to-one if (and only if) its image in the parameter space is such that all parametric triangles have a positive area. We then derive a non-standard linear discretization scheme based on mean value coordinates to compute such one-toone parametrizations, and show that the scheme does not discretize a Laplacian on a structured mesh. The proposed pipeline is implemented in the open source mesh generator Gmsh, where the creation of suitable patches is based on triangulation topology and parametrization quality, combined with feature edge detection. Several examples illustrate the robustness of the resulting implementation.

Indirect all-quadrilateral meshing based on bipartite topological labeling

“…Meshing complex models with a parameter space approach does not allow to globally align a mesh with a cross-field, since each discrete patch of a CAD model may be equipped with an independent parametrization and the feature edges that separate those patches are not necessary aligned with the cross-field. Parametrization techniques can also be used to remesh triangulations [8,9].…”

Method of Real-Time Wellbore Surface Reconstruction Based on Spiral Contour

“…However, these are only used if the number of points m is not too different from the number of points n. When there is a big difference between m and n, the regions of the point set with fewer points correspond to multiple edges on the point set with more points, and the constructed 3D structure becomes rough, and, in some instances, even loses the characteristics of the structure itself [8][9][10][11][12]. Another method is to use the Delaunay irregular triangulation mesh to realize the segmentation and modeling of discrete data points in space [13][14][15]. For a uniform set of spatial points, the technology of using Delaunay triangulation to form a spatial surface is relatively mature.…”

“…For example, in real wellbore surface scan data, due to the fast drilling process, the data points are sometimes dense, and other times sparse and uneven. When the set of points on the borehole wall is very sparse, the Delaunay subdivision may treat the sparse points on the Another method is to use the Delaunay irregular triangulation mesh to realize the segmentation and modeling of discrete data points in space [13][14][15]. For a uniform set of spatial points, the technology of using Delaunay triangulation to form a spatial surface is relatively mature.…”

Automatic generation of global shell-element meshes for large-scale structural design optimization

“…Some prior work has also been done to use the parameterization of surface patches to generate quadrilateral meshes by initializing the mesh in the parametric domain, then do the smoothing and project the mesh back to physical domain. [13][14][15]. After the projection, some post-processing steps may be implemented to improve the mesh quality.…”