四面体网格边界恢复改进算法

Improved boundary recovery method for tetrahedral mesh generation

  • 摘要: Delaunay三角化是生成四面体网格的主流方法,而通过该方法生成的初始网格无法保留所有边界约束,因此边界恢复是Delaunay四面体网格生成的必要步骤。边界恢复的难点在于确定辅助点(Steiner点)的数量和位置,以及降低Steiner点引发的负面效应。为此,本文提出了一种改进的四面体网格边界恢复方法,旨在提高约束边界恢复成功率,并减少加入的Steiner点数量。该方法总体流程由“两层+两轮”迭代构成,流程充分利用了约束边界恢复方法和体内Steiner点插入方法的优势,降低了边界恢复对边界约束的破坏。方法首先针对递归壳变换算法容易陷入局部最优解的问题,通过引入模拟退火算法加以解决,提出了一种改进的约束边界恢复方法;然后对于方法中的“网格实体—边界实体求交”关键环节,引入或实现了AABB树、几何精确的“线面相交”函数、交点数查询哈希算法三个关键方法加以优化;最后对于拓扑变换无法恢复的边界,实现了体内、边界两种Steiner点插入方法。实验阶段取用了Thingi10k数据集的4000余例面网格样本进行测试,结果表明该方法有效提高了约束边界恢复的成功率,并能普遍性地减少边界恢复引入的Steiner点数量。

     

    Abstract: Delaunay triangulation is a mainly used method for tetrahedral mesh generation, but the initial mesh generated by this method cannot include all boundary constraints, so the boundary recovery is a necessary step for the generation of Delaunay tetrahedral mesh. The difficulty of boundary recovery lies in determining the number and location of auxiliary points (Steiner points) and reducing the negative effects caused by Steiner points. In this study, an improved boundary recovery method for Delaunay tetrahedral mesh generation is proposed, which aims to increase the success rate of constrained recovery and reduce the number of Steiner points added during the boundary recovery. The overall process of this method is composed of a double iteration with two rounds inside, which fully utilizes the advantages of the constrained boundary recovery method and the interior Steiner point insertion method, and reduces the number of broken boundary constraints caused by boundary restoration. This method firstly solves the problem that the recursive shell transformation algorithm tends to fall into the local optimum, by introducing the simulated annealing algorithm, and an improved constrained boundary recovery method is proposed. Then, three key methods, including the AABB tree, the geometrically accurate "line and surface intersection" function, and a hash algorithm for intersection count query, are introduced or proposed to improve the efficiency and robustness of finding the intersection between mesh entities and boundary entities. Finally, for boundaries that cannot be recovered by topological transformation, the interior and boundary Steiner points are inserted. The proposed method is tested on more than 4,000 surface mesh samples of the Thingi10k dataset, which shows that the success rate of constrained boundary recovery is effectively improved, and meanwhile the number of Steiner points introduced by the boundary recovery is generally reduced.

     

/

返回文章
返回