Singularity Structure Simplification of Hexahedral Mesh via Weighted Ranking

TL;DR

This paper introduces a weighted ranking method for simplifying singularity structures in hexahedral meshes, improving mesh quality and convergence over traditional thickness-based approaches.

Contribution

The paper proposes a novel weighted ranking function combining local singularity valence, shape quality, and sheet width for better singularity structure simplification.

Findings

Fewer base-complex components with the new method.

Achieves comparable Hausdorff distance ratio.

Improves mesh element uniformity and aspect ratio.

Abstract

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.