面向脏几何的曲面网格自动生成算法

Auto-generation algorithm of surface meshes on dirty geometries

脏几何是存在法向错误、穿插、狭缝、贴合等问题的几何模型,在此类模型的原始边界上直接生成网格无法避免上述问题。因此,在脏几何上无法直接生成拓扑相容的表面网格,这也将影响后续数值分析研究的开展。本文实现了一种基于四面体化方法的脏几何网格生成算法,其核心思想在于一个有效的四面体网格的表面一定是一个有效的曲面网格。本文对几何的离散表征进行法向修复,并在此基础上生成四面体网格,通过离散边界切割四面体解决了模型中存在的穿插问题,基于四面体质量提升解决狭缝问题,并应用曲面网格重构以提升表面网格质量。本文采用视图采样的方法实现法向修复,从多个方向观察该模型,使其在各个方向上的视图均满足质量要求;使用多级的能量阈值提升四面体优化效率;采用多级误差估计来避免曲面网格重构中可能出现自相交的问题。数值验证结果表明本文的脏几何曲面网格自动生成算法鲁棒、高效。

Dirty geometry is a geometric model with issues such as normal errors, intersections, slits and overlaps, which are unavoidable for generating meshes directly on the original boundaries. As a result, it is challenging to directly generate topologically compatible surface meshes on dirty geometries, and subsequent numerical analyses can thus be affected. The present study implements a dirty geometry mesh generation algorithm based on tetrahedral meshes, and the core idea of the algorithm is that the surface of an effective tetrahedral mesh must be an effective curved one. Our method performs normal repairment on discrete representations to generate tetrahedral meshes, solves the intersection via cutting tetrahedrons by discrete boundaries, and eliminates slits based on tetrahedron quality optimization. The surface mesh quality is further improved with surface remeshing under the guidance of the geometry size. The view sampling method is used to achieve normal restoration and fulfil the quality requirements in all directions. The multi-level energy thresholds are adopted to improve the efficiency of the tetrahedral optimization. Numerical test results suggest that the present auto-generation algorithm of curved surface meshes on dirty geometries is robust and efficient.