Local Decomposition of Hexahedral Singular Nodes into Singular Curves. (May 2023) - Zhang, Paul; Chiang, Judy (Hsin-Hui); Fan, Xinyi (Cynthia); Mundilova, Klara
Abstract: Hexahedral (hex) meshing is a long studied topic in geometry processing with many challenging associated problems. Hex meshes vary from structured to unstructured depending on application or domain of interest. Fully structured meshes require that all interior mesh edges be adjacent to four hexes each. Edges failing this criteria are 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. Hex meshes 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. Graphical abstract: Highlights: Explicit construction of singular decomposition for eight most common singular nodes. Proof that all singular nodes are locally decomposable. Algorithm and demonstration for singular decomposition on various hexahedral meshes.