Hexahedral Mesh Structure Visualization and Evaluation

Abstract

Understanding hexahedral (hex-) mesh structures is important for a number of hex-mesh generation and optimization tasks. However, due to various configurations of the singularities in a valid pure hex-mesh, the structure (or base complex) of the mesh can be arbitrarily complex. In this work, we present a first and effective method to help meshing practitioners understand the possible configurations in a valid 3D base complex for the characterization of their complexity. In particular, we propose a strategy to decompose the complex hex-mesh structure into multi-level sub-structures so that they can be studied separately, from which we identify a small set of the sub-structures that can most efficiently represent the whole mesh structure. Furthermore, from this set of sub-structures, we attempt to define the first metric for the quantification of the complexity of hex-mesh structure. To aid the exploration of the extracted multi-level structure information, we devise a visual exploration system coupled with a matrix view to help alleviate the common challenge of 3D data exploration (e.g., clutter and occlusion). We have applied our tool and metric to a large number of hex-meshes generated with different approaches to reveal different characteristics of these methods in terms of the mesh structures they can produce. We also use our metric to assess the existing structure simplification techniques in terms of their effectiveness.

Integral Curve Clustering and Simplification for Flow Visualization: A Comparative Evaluation

“…We use a ranking-based visualization technique similar to what has been applied in hex-mesh quality visualization in [84] for two evaluation matrices. Firstly, we map all four evaluation matrices to the range [0.1, 1.0] so that 0.1 always denotes the worst value and 1.0 for the best, e.g., largest silhouette value and smallest validity marked as 1.0.…”

Interactive Focus+Context Rendering for Hexahedral Mesh Inspection

“…Recently, [7] proposed to visualize the mesh structure of hexahedral meshes by using a subset of the most important base-complex sheets and dual chords, and show their interrelation using adjacency matrices. We take inspiration from their approach utilizing basecomplex mesh sheets to reduce the structural complexity of a mesh (cf.…”

“…In an iterative process, pairs of sheet components are merged into a joint component until no components can be merged anymore. Therefore, for all pairs of sheet components, their neighborhood relation is classified analogously to the work by [7] as • adjacent (or tangent),…”

“…Furthermore, peeling and filtering can make it difficult to maintain the global mesh structure and spatial relationships between mesh regions with different properties. The latter problem has been addressed by Xu and Chen [7] via the computation of a global topological mesh structure, which is decomposed into a set of contiguous sub-structures to support a part-based topological complexity analysis.…”

HexaLab.net: An online viewer for hexahedral meshes

“…Improved visualization of the global structure: currently, Hexa-Lab highlights irregular edges, but additional mechanisms could be used to communicate the global structure of the inspected hex-mesh. For example, future versions could compute and use the base complex, or integrate the advanced visualization methods proposed in [79], which target the visualization of the (potentially intricate) whole structure of a hex-mesh. Dynamic datasets: currently, HexaLab only supports static meshes.…”