论文标题
离散模型的自动表面网格生成：基于重新聚集的完整和自动管道
Automatic surface mesh generation for discrete models: A complete and automatic pipeline based on reparameterization
论文作者
论文摘要
三角剖分是有限元社区的无处不在的输入。但是，对于有限元分析而言，通过成像技术获得的大多数原始三角剖分是不合适的。在本文中，我们根据自动选择的输入三角形贴片的一对一参数化提供了强大的管道来处理这些三角形，这使得每个贴片都可以通过标准有限元元素介绍算法来弥补。仅使用几何参数，我们证明，当（仅当）其在参数空间中的图像使所有参数三角形都具有正面区域时，贴片的离散参数化是一对一的。然后，我们基于平均值坐标来得出一个非标准的线性离散方案以计算这种一对一的参数化，并表明该方案不会在结构化网格上离散laplacian。所提出的管道在开源网格发电机GMSH中实现，其中合适的贴片的创建基于三角拓扑和参数化质量，并结合了特征边缘检测。几个示例说明了由此产生的实现的鲁棒性。
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-to-one 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.
