Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Zhang, Paul; Chiang, Judy (Hsin-Hui); Fan, Xinyi (Cynthia); Mundilova, Klara

doi:10.1016/j.cad.2023.103484

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Journal Article · Mon Feb 06 00:00:00 EST 2023 · Computer Aided Design

DOI:https://doi.org/10.1016/j.cad.2023.103484· OSTI ID:2424515

^[1]; Chiang, Judy (Hsin-Hui) ^[2]; Fan, Xinyi (Cynthia) ^[3]; Mundilova, Klara ^[1]

Massachusetts Institute of Technology, Cambridge, MA (United States)
University of Illinois at Urbana-Champaign, IL (United States)
Davidson College, NC (United States)

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. In conclusion, with this decomposition, the enigmatic complexity of 3D singular nodes becomes effectively 2D.

View Accepted Manuscript (DOE)

Research Organization:: University of Illinois at Urbana-Champaign, IL (United States)

Sponsoring Organization:: Army Research Office; National Science Foundation (NSF); USDOE

OSTI ID:: 2424515

Alternate ID(s):: OSTI ID: 1924564

Journal Information:: Computer Aided Design, Journal Name: Computer Aided Design Vol. 158; ISSN 0010-4485

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (17)

Topological modifications of hexahedral meshes via sheet operations: a theoretical study Ledoux, Franck; Shepherd, Jason Engineering with Computers, Vol. 26, Issue 4 https://doi.org/10.1007/s00366-009-0145-2	journal	November 2009
A performance study of tetrahedral and hexahedral elements in 3-D finite element structural analysis Cifuentes, A. O.; Kalbag, A. Finite Elements in Analysis and Design, Vol. 12, Issue 3-4 https://doi.org/10.1016/0168-874X(92)90040-J	journal	December 1992
HexaLab.net: An online viewer for hexahedral meshes Bracci, Matteo; Tarini, Marco; Pietroni, Nico Computer-Aided Design, Vol. 110 https://doi.org/10.1016/j.cad.2018.12.003	journal	May 2019
Singularity Structure Simplification of Hexahedral Meshes via Weighted Ranking Xu, Gang; Ling, Ran; Zhang, Yongjie Jessica Computer-Aided Design, Vol. 130 https://doi.org/10.1016/j.cad.2020.102946	journal	January 2021
Refinable smooth surfaces for locally quad-dominant meshes with T-gons Karčiauskas, Kȩstutis; Peters, Jörg Computers & Graphics, Vol. 82 https://doi.org/10.1016/j.cag.2019.05.013	journal	August 2019
Minimal bi-6 G2 completion of bicubic spline surfaces Karčiauskas, Kȩstutis; Peters, Jörg Computer Aided Geometric Design, Vol. 41 https://doi.org/10.1016/j.cagd.2015.10.005	journal	January 2016
The topological theory of defects in ordered media Mermin, N. D. Reviews of Modern Physics, Vol. 51, Issue 3 https://doi.org/10.1103/RevModPhys.51.591	journal	July 1979
Frame Field Singularity Correctionfor Automatic Hexahedralization Jiang, Tengfei; Huang, Jin; Wang, Yuanzhen IEEE Transactions on Visualization and Computer Graphics, Vol. 20, Issue 8 https://doi.org/10.1109/TVCG.2013.250	journal	August 2014
CubeCover- Parameterization of 3D Volumes Nieser, M.; Reitebuch, U.; Polthier, K. Computer Graphics Forum, Vol. 30, Issue 5 https://doi.org/10.1111/j.1467-8659.2011.02014.x	journal	August 2011
Connectivity editing for quadrilateral meshes Peng, Chi-Han; Zhang, Eugene; Kobayashi, Yoshihiro Proceedings of the 2011 SIGGRAPH Asia Conference https://doi.org/10.1145/2024156.2024175	conference	December 2011
All-hex meshing using singularity-restricted field Li, Yufei; Liu, Yang; Xu, Weiwei ACM Transactions on Graphics, Vol. 31, Issue 6 https://doi.org/10.1145/2366145.2366196	journal	November 2012
Hexahedral mesh re-parameterization from aligned base-complex Gao, Xifeng; Deng, Zhigang; Chen, Guoning ACM Transactions on Graphics, Vol. 34, Issue 4 https://doi.org/10.1145/2766941	journal	July 2015
HexEx Lyon, Max; Bommes, David; Kobbelt, Leif ACM Transactions on Graphics, Vol. 35, Issue 4 https://doi.org/10.1145/2897824.2925976	journal	July 2016
Practical 3D frame field generation Ray, Nicolas; Sokolov, Dmitry; Lévy, Bruno ACM Transactions on Graphics, Vol. 35, Issue 6 https://doi.org/10.1145/2980179.2982408	journal	November 2016
Boundary Element Octahedral Fields in Volumes Solomon, Justin; Vaxman, Amir; Bommes, David ACM Transactions on Graphics, Vol. 36, Issue 3 https://doi.org/10.1145/3065254	journal	May 2017
Symmetric moving frames Corman, Etienne; Crane, Keenan ACM Transactions on Graphics, Vol. 38, Issue 4 https://doi.org/10.1145/3306346.3323029	journal	July 2019
Seamless Parametrization with Arbitrary Cones for Arbitrary Genus Campen, Marcel; Shen, Hanxiao; Zhou, Jiaran ACM Transactions on Graphics, Vol. 39, Issue 1 https://doi.org/10.1145/3360511	journal	December 2019

Similar Records

The generation of hexahedral meshes for assembly geometries: A survey

Journal Article · Sun Feb 13 23:00:00 EST 2000 · International Journal for Numberical Methods in Engineering · OSTI ID:751248

Integration of Mesh Optimization with 3D All-Hex Mesh Generation, LDRD Subcase 3504340000, Final Report

Technical Report · Sun Oct 31 23:00:00 EST 1999 · OSTI ID:14930

Connectivity-based, all-hexahedral mesh generation method and apparatus

Patent · Tue Jun 16 00:00:00 EDT 1998 · OSTI ID:672605

Related Subjects

97 MATHEMATICS AND COMPUTING
Computational geometry
Computer Science
Hexahedral mesh
Singular graph

Local Decomposition of Hexahedral Singular Nodes into Singular Curves

Citation Formats

References (17)

Similar Records

Related Subjects