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Automatic feature-preserving size field for 3D mesh generation
arXiv - CS - Computational Geometry Pub Date : 2020-09-04 , DOI: arxiv-2009.03984
Arthur Bawin, Fran\c{c}ois Henrotte, Jean-Fran\c{c}ois Remacle

This paper presents a methodology aiming at easing considerably the generation of high-quality meshes for complex 3D domains. We show that the whole mesh generation process can be controlled with only five parameters to generate in one stroke quality meshes for arbitrary geometries. The main idea is to build a meshsize field $h(x)$ taking local features of the geometry, such as curvatures, into account. Meshsize information is then propagated from the surfaces into the volume, ensuring that the magnitude of $\vert \nabla h \vert$ is always controlled so as to obtain a smoothly graded mesh. As the meshsize field is stored in an independent octree data structure, the function h can be computed separately, and then plugged in into any mesh generator able to respect a prescribed meshsize field. The whole procedure is automatic, in the sense that minimal interaction with the user is required. Applications examples based on models taken from the very large ABC dataset, are then presented, all treated with the same generic set of parameter values, to demonstrate the efficiency and the universality of the technique.

中文翻译:

用于 3D 网格生成的自动特征保留大小字段

本文提出了一种方法,旨在大大简化复杂 3D 域的高质量网格的生成。我们表明,整个网格生成过程可以只用五个参数来控制,以便为任意几何形状生成一个笔划质量的网格。主要思想是建立一个网格大小的场 $h(x)$ 考虑几何的局部特征,例如曲率。然后将网格大小信息从表面传播到体积中,确保始终控制 $\vert \nabla h \vert$ 的大小,以获得平滑分级的网格。由于网格大小字段存储在独立的八叉树数据结构中,因此可以单独计算函数 h,然后将其插入任何能够遵守指定网格大小字段的网格生成器中。整个过程是自动的,从某种意义上说,需要与用户进行最少的交互。然后呈现基于从非常大的 ABC 数据集获取的模型的应用示例,所有示例都使用相同的通用参数值集进行处理,以证明该技术的效率和通用性。
更新日期:2020-09-10
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