Tetrahedral Meshing in the Wild
Tetrahedral Meshing in the Wild
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DOI：
10.1145/3197517.3201353
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发表时间：
2018-08-01
影响因子：
6.2
通讯作者：
Panozzo, Daniele
中科院分区：
文献类型：
--
作者：
Hu, Yixin;Zhou, Qingnan;Panozzo, Daniele
我们提出一种新颖的四面体网格划分技术，它具有无条件的稳健性，无需用户交互，并且能够直接将三角形集合转换为可用于分析的体网格。该方法基于几个核心原则：（1）基于完全稳健且高效的滤波精确计算进行初始网格构建；（2）对网格相对于表面输入进行明确的（自动或用户定义的）公差设定；（3）在每一步都保证输出有效性的迭代网格改进。所得网格的质量是目标网格尺寸和允许公差的直接函数：增加与初始网格的允许偏差以及减小目标边长都会导致更高的网格质量。我们的方法实现了“黑箱”分析，即它允许在任意几何模型上自动求解偏微分方程，提供了与例如图像处理算法相当的稳健性和可靠性，为现实世界几何数据的自动、大规模处理打开了大门。
We propose a novel tetrahedral meshing technique that is unconditionally robust, requires no user interaction, and can directly convert a triangle soup into an analysis-ready volumetric mesh. The approach is based on several core principles: (1) initial mesh construction based on a fully robust, yet efficient, filtered exact computation (2) explicit (automatic or user-defined) tolerancing of the mesh relative to the surface input (3) iterative mesh improvement with guarantees, at every step, of the output validity. The quality of the resulting mesh is a direct function of the target mesh size and allowed tolerance: increasing allowed deviation from the initial mesh and decreasing the target edge length both lead to higher mesh quality.Our approach enables "black-box" analysis, i.e. it allows to automatically solve partial differential equations on geometrical models available in the wild, offering a robustness and reliability comparable to, e.g., image processing algorithms, opening the door to automatic, large scale processing of real-world geometric data.