Hexahedral Mesh Generation via Closed-Form Polycube
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Solution Overview
Problem
Conventional hexahedral mesh generation methods face challenges in automation, user control, and achieving high-quality meshes for complex models, particularly those with complex topological structures, due to limitations in initial orientation assumptions and global degradation issues.
Innovation Solution
A method is developed to generate hexahedral meshes based on closed-form polycubes by converting triangular meshes to tetrahedral meshes, establishing a smooth frame field, and optimizing it using L1-based polycube generation, allowing for user-controlled surface normal alignment and internal frame field smoothness, which results in a high-quality mesh independent of the model's initial position.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If polycube-based hexahedral mesh generation is used, then automation is improved, but user control capability deteriorates
Solution Approach 1:
The system dynamically adjusts between automated polycube generation and user-controlled refinement. Users can intervene at specific stages (e.g., handle detection, cut surface definition, frame field optimization) to guide the mesh generation process while maintaining overall automation. This dynamic interaction resolves the contradiction by allowing both automated processing and user control depending on the stage and user needs.
2Adaptability or versatility
If conventional polycube methods are used for complex models, then processing capability is improved, but mesh quality deteriorates
Solution Approach 1:
The patent applies local quality optimization by introducing frame fields with singularity restrictions at specific locations. Instead of uniform mesh generation, the method locally adjusts the frame field properties around handles and complex features to maintain high mesh quality in critical regions while preserving overall processing capability for complex models.
Solution Approach 2:
The method changes parameters by optimizing frame field configurations and singularity placements based on local geometric features. By adjusting frame field parameters and singularity locations adaptively, the system maintains high mesh quality for complex models with varying topological structures while preserving general processing capability.
3Manufacturing precision
If grid modification operations are performed for global degradation, then mesh generation is improved, but robustness deteriorates
Solution Approach 1:
The patent performs preliminary actions by pre-detecting handles and pre-defining cut surfaces before mesh generation. This preliminary preparation ensures that the polycube decomposition is performed correctly from the start, avoiding the need for subsequent grid modification operations to fix global degradation issues, thereby maintaining robustness while achieving good mesh generation results.
Data Source
AI summary
A method for generating a hexahedral mesh based on a closed-form polycube includes steps of: converting a surface triangular mesh into a tetrahedral mesh; obtaining an initial 3-dimensional frame field; according surface normal constraint, generating a smooth frame field without singular line inside the model; extracting a transition relation on the cut surface based on the smooth frame field; providing Poisson optimization on cut model based on the frame field for obtaining a preliminary parameterized result; using L1-optimization for forming a final closed-form polycube; optimizing with an mixed integer for obtaining a final parameterized result; and extracting the hexahedral mesh. The method automatically generates the hexahedral mesh from the triangular mesh, and has nothing to do with an initial position of an object, which is able to better satisfy a characteristic constraint of the model; and for a model with complex topology, high quality hexahedral mesh is available.