Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially 3 new active faces are created. This methodology is the underpinnings of our last resort method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved.

中文翻译：

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使用局部拓扑变换对 Delaunay 四面体网格进行边界恢复


存在许多高质量的体积网格生成系统。然而，没有任何策略可以在不损害某些元素质量的情况下解决所有几何情况。许多 3D 网格生成算法基于 Delaunay 四面体化，这种算法经常无法保留输入边界表面拓扑。对于生物医学应用，这种表面保护至关重要，因为它们通常包含多个连贯连接的感兴趣材料区域。在本文中，我们提出了一种算法作为后处理方法，该方法可以优化元素质量受损的局部区域并恢复原始边界面面（三角形），而不管原始网格生成策略如何。该算法在缺失的边界面或受损元素附近雕刻出一个小子体积，从而创建一个空腔。如果任务是恢复表面边界面，则空腔中将存在自然出口孔。首先用缺失的边界面修补该孔，然后用其他修补剂来密封空腔。如果任务是改善受损区域，那么空腔已经被密封。腔壳的每个三角形面都被归类为活动面，并且可以连接到另一个壳节点以创建四面体。在此过程中，四面体的底面将从活动面列表中删除，并可能创建 3 个新的活动面。这种方法是我们最后手段的基础。每个活动面都可以被视为一棵树的树干。详尽的呼吸和深度搜索将识别所有可能的四面体组合以独特地填充空腔。我们简化了这个递归过程，将时间复杂度降低了几个数量级。 原始表面边界（内部和外部）得到完全恢复，受损区域的质量得到改善。