Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the ${\mathcal{L}}^1$ error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method.

尽管在提高四面体网格质量方面取得了巨大成功，但最初的最优德劳内三角剖分 (ODT) 旨在仅移动内部顶点，因此无法处理边界上包含“坏”三角形的输入网格。在当前的工作中，我们提出了一种称为边界优化 Delaunay 三角剖分 (B-ODT) 的集成方法来平滑（改进）四面体网格。在我们的方法中，内部和边界顶点都通过分析最小化来重新定位${\mathcal{升}}^1$抛物面函数与其在每个顶点邻域上的分段线性插值之间的误差。除了保证体积保留特性之外，所提出的算法可以很容易地适应以保留原始网格中的锐利特征。包括许多实验来证明我们方法的性能。