基于八叉树细化的高效四面体网格生成

Efficient tetrahedral mesh generation algorithm based on octree refinement

  • 摘要: 非结构化网格是一种在计算机辅助工程和计算机图形学中广泛应用的网格类型,相对于结构化网格可以更好地适应复杂几何形状。当前的非结构化四面体网格生成方法多数需要先生成表面网格,再基于表面网格生成体网格,在大型复杂模型的高精度仿真中往往会出现三维网格生成出错或规模过大的情况,在生成效率方面难以有较大突破。为了克服现有技术中网格生成效率低、鲁棒性较差、实现过程复杂等缺陷,提出了一种基于八叉树细化的非结构化四面体网格生成算法。测试结果表明,该算法能够高效地生成高质量网格,并克服了传统方法的局限性,为非结构化四面体网格生成领域的研究和应用提供了新的思路和参考。

     

    Abstract: Compared with structured meshes, non-structured meshes can better adapt to complex geometric shapes, and are widely used in computer-aided engineering and computer graphics. Efficient mesh generation algorithms enhance engineering productivity while mitigating errors and costs associated with manual operations. Unstructured grids, unlike structured grids, offer superior adaptability to intricate geometric shapes, making them widely employed in computer-aided engineering and computer graphics. Currently, non-structured tetrahedral mesh generation methods often require the generation of a surface mesh first, followed by the generation of a volume mesh based on the surface mesh. This approach can lead to errors in three-dimensional mesh generation or an excessive number of grids in high-precision simulations of large and complex models, making it difficult to significantly improve generation efficiency. Furthermore, high-quality grids are crucial for enhancing the accuracy and stability of numerical computations since poor grid quality amplifies numerical errors and may even induce instability. To address the shortcomings of existing techniques, this paper proposes an octree-based refinement algorithm for generating unstructured tetrahedral grids. The octree grid generation algorithm leverages spatial decomposition to generate grids. Specifically, the algorithm initially recursively subdivides each hexahedral unit into eight, and subsequently converts the interior and boundary units of the hexahedra into tetrahedral units. This paper provides a comprehensive exposition of the two key generation steps: initial octree grid generation and surface fitting. The algorithm employs an improved root tetrahedral grid shape, streamlining the initial octree grid generation process while ensuring consistent shapes of initial grid units. Additionally, the surface fitting stage incorporates grid shape adjustment and grid splitting. Experimental results demonstrate that the proposed algorithm effectively handles certain geometric model defects and exhibits notable advantages in terms of grid generation quality and efficiency. Overall, this algorithm introduces new perspectives and references for research and applications in the field of unstructured tetrahedral grid generation.

     

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