216 research outputs found
Frame Fields for Hexahedral Mesh Generation
As a discretized representation of the volumetric domain, hexahedral meshes have been a popular choice in computational engineering science and serve as one of the main mesh types in leading industrial software of relevance. The generation of high quality hexahedral meshes is extremely challenging because it is essentially an optimization problem involving multiple (conflicting) objectives, such as fidelity, element quality, and structural regularity. Various hexahedral meshing methods have been proposed in past decades, attempting to solve the problem from different perspectives. Unfortunately, algorithmic hexahedral meshing with guarantees of robustness and quality remains unsolved.
The frame field based hexahedral meshing method is the most promising approach that is capable of automatically generating hexahedral meshes of high quality, but unfortunately, it suffers from several robustness issues. Field based hexahedral meshing follows the idea of integer-grid maps, which pull back the Cartesian hexahedral grid formed by integer isoplanes from a parametric domain to a surface-conforming hexahedral mesh of the input object. Since directly optimizing for a high quality integer-grid map is mathematically challenging, the construction is usually split into two steps: (1) generation of a feature-aligned frame field and (2) generation of an integer-grid map that best aligns with the frame field. The main robustness issue stems from the fact that smooth frame fields frequently exhibit singularity graphs that are inappropriate for hexahedral meshing and induce heavily degenerate integer-grid maps. The thesis aims at analyzing the gap between the topologies of frame fields and hexahedral meshes and developing algorithms to realize a more robust field based hexahedral mesh generation.
The first contribution of this work is an enumeration of all local configurations that exist in hexahedral meshes with bounded edge valence and a generalization of the Hopf-Poincaré formula to octahedral (orthonormal frame) fields, leading to necessary local and global conditions for the hex-meshability of an octahedral field in terms of its singularity graph. The second contribution is a novel algorithm to generate octahedral fields with prescribed hex-meshable singularity graphs, which requires the solution of a large non-linear mixed-integer algebraic system. This algorithm is an important step toward robust automatic hexahedral meshing since it enables the generation of a hex-meshable octahedral field.
In the collaboration work with colleagues [BRK+22], the dataset HexMe consisting of practically relevant models with feature tags is set up, allowing a fair evaluation for practical hexahedral mesh generation algorithms. The extendable and mutable dataset remains valuable as hexahedral meshing algorithms develop. The results of the standard field based hexahedral meshing algorithms on the HexMesh dataset expose the fragility of the automatic pipeline.
The major contribution of this thesis improves the robustness of the automatic field based hexahedral meshing by guaranteeing local meshability of general feature aligned smooth frame fields. We derive conditions on the meshability of frame fields when feature constraints are considered, and describe an algorithm to automatically turn a given non-meshable frame field into a similar but locally meshable one. Despite the fact that local meshability is only a necessary but not sufficient condition for the stronger requirement of meshability, our algorithm increases the 2% success rate of generating valid integer-grid maps with state-of-the-art methods to 57%, when compared on the challenging HexMe dataset
Hybrid Base Complex: Extract and Visualize Structure of Hex-dominant Meshes
Hex-dominant mesh generation has received significant attention in recent
research due to its superior robustness compared to pure hex-mesh generation
techniques. In this work, we introduce the first structure for analyzing
hex-dominant meshes. This structure builds on the base complex of pure
hex-meshes but incorporates the non-hex elements for a more comprehensive and
complete representation. We provide its definition and describe its
construction steps. Based on this structure, we present an extraction and
categorization of sheets using advanced graph matching techniques to handle the
non-hex elements. This enables us to develop an enhanced visual analysis of the
structure for any hex-dominant meshes.We apply this structure-based visual
analysis to compare hex-dominant meshes generated by different methods to study
their advantages and disadvantages. This complements the standard quality
metric based on the non-hex element percentage for hex-dominant meshes.
Moreover, we propose a strategy to extract a cleaned (optimized) valence-based
singularity graph wireframe to analyze the structure for both mesh and sheets.
Our results demonstrate that the proposed hybrid base complex provides a coarse
representation for mesh element, and the proposed valence singularity graph
wireframe provides a better internal visualization of hex-dominant meshes.Comment: accepted by IEEE Transactions on Visualization and Computer Graphic
HybridOctree_Hex: Hybrid Octree-Based Adaptive All-Hexahedral Mesh Generation with Jacobian Control
We present a new software package, "HybridOctree_Hex," for adaptive
all-hexahedral mesh generation based on hybrid octree and quality improvement
with Jacobian control. The proposed HybridOctree_Hex begins by detecting
curvatures and narrow regions of the input boundary to identify key surface
features and initialize an octree structure. Subsequently, a strongly balanced
octree is constructed using the balancing and pairing rules. Inspired by our
earlier preliminary hybrid octree-based work, templates are designed to
guarantee an all-hexahedral dual mesh generation directly from the strongly
balanced octree. With these pre-defined templates, the sophisticated hybrid
octree construction step is skipped to achieve an efficient implementation.
After that, elements outside and around the boundary are removed to create a
core mesh. The boundary points of the core mesh are connected to their
corresponding closest points on the surface to fill the buffer zone and build
the final mesh. Coupled with smart Laplacian smoothing, HybridOctree_Hex takes
advantage of a delicate optimization-based quality improvement method
considering geometric fitting, Jacobian and scaled Jacobian, to achieve a
minimum scaled Jacobian that is higher than . We empirically verify the
robustness and efficiency of our method by running the HybridOctree_Hex
software on dozens of complex 3D models without any manual intervention or
parameter adjustment. We provide the HybridOctree_Hex source code, along with
comprehensive results encompassing the input and output files and statistical
data in the following repository: https://github.com/CMU-CBML/HybridOctree_Hex
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