论文标题

六面体单数节点的局部分解成奇异曲线

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

论文作者

Zhang, Paul, Chiang, Judy Hsin-Hui, Xinyi, Fan, Mundilova, Klara

论文摘要

六面体(HEX)网格划分是几何处理中的长期研究主题,并且有许多有趣且具有挑战性的相关问题。十六进制的筛网在复杂性上从结构化到非结构化,具体取决于应用或感兴趣的领域。完全结构化的网格要求所有内部网格边缘恰好与四个HEXE相邻。不满足此标准的边缘被认为是单数,并表示非结构化的十六进制网格。奇异边缘将形成封闭循环的单数曲线融为一体,在网格边界上结束,或以一个单数节点结束,这是一个超过两个奇异曲线的复杂连接。尽管所有具有奇异性的十六进制网格都是非结构化的,但是那些具有更复杂的奇异节点的人往往具有更扭曲的元素和较小的雅各布值。在这项工作中,我们研究了单数节点的拓扑。我们表明,所有八个最常见的单数节点都可以分解为单数曲线。我们进一步表明,所有单数节点,无论边缘价如何,都可以局部分解。最后,我们在十六进制网格上演示了这些分解,从而减少了它们的失真并将所有奇异节点转换为单数曲线。通过这种分解,3D单数节点的神秘复杂性实际上变成2D。

Hexahedral (hex) meshing is a long studied topic in geometry processing with many fascinating and challenging associated problems. Hex meshes vary in complexity from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges are adjacent to exactly four hexes. Edges not satisfying this criteria are considered singular and indicate an unstructured hex mesh. Singular edges join together into singular curves that either form closed cycles, end on the mesh boundary, or end at a singular node, a complex junction of more than two singular curves. While all hex meshes with singularities are unstructured, those with more complex singular nodes tend to have more distorted elements and smaller scaled Jacobian values. In this work, we study the topology of singular nodes. We show that all eight of the most common singular nodes are decomposable into just singular curves. We further show that all singular nodes, regardless of edge valence, are locally decomposable. Finally we demonstrate these decompositions on hex meshes, thereby decreasing their distortion and converting all singular nodes into singular curves. With this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

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