Singularity Structure Simplification of Hexahedral Mesh via Weighted Ranking

• Main Authors: Xu, Gang, Ling, Ran, Zhang, Jessica, Xiao, Zhoufang, Ji, Zhongping, Rabczuk, Timon
• Format: Journal Article
• Language: English
• Published: 01-01-2019
• Subjects: Computer Science - Computational Geometry; Computer Science - Graphics
• DOI: 10.48550/arxiv.1901.00238

In this paper, we propose an improved singularity structure simplification
method for hexahedral (hex) meshes using a weighted ranking approach. In
previous work, the selection of to-be-collapsed base complex sheets/chords is
only based on their thickness, which will introduce a few closed-loops and
cause an early termination of simplification and a slow convergence rate. In
this paper, a new weighted ranking function is proposed by combining the
valence prediction function of local singularity structure, shape quality
metric of elements and the width of base complex sheets/chords together.
Adaptive refinement and local optimization are also introduced to improve the
uniformity and aspect ratio of mesh elements. Compared to thickness ranking
methods, our weighted ranking approach can yield a simpler singularity
structure with fewer base-complex components, while achieving comparable
Hausdorff distance ratio and better mesh quality. Comparisons on a hex-mesh
dataset are performed to demonstrate the effectiveness of the proposed method.