Quadrilateral Mesh Singularity Reduction via Minimum Templates
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Solution Overview
Problem
Current methods for generating quadrilateral meshes struggle to achieve both high geometric and topological quality, leading to numerical instability and other issues in applications like computational fluid dynamics and graphics, due to the presence of singularities, which are difficult to control and optimize.
Innovation Solution
The method involves replacing sub-meshes with Minimum Singularity Templates (MSTs) using a process that identifies and ranks singularities, applies a shortest path algorithm, and performs a breadth-first search to determine patches, which are then replaced with optimized templates to reduce singularities while maintaining geometric quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If automatic mesh generators are used to produce high geometric quality mesh, then geometric quality is improved, but topological quality deteriorates due to low optimization with respect to singularities
Solution Approach 1:
The mesh is divided into patches, and singularities are identified and treated locally within each patch. The algorithm segments the mesh into regions with singularities and regions without, allowing targeted optimization of topological quality in singularity-prone areas while preserving geometric quality achieved by automatic mesh generators.
Solution Approach 2:
The invention changes the parameter of singularity count in patches by applying operations that reduce singularities. By systematically reducing the number of singularities in each patch while maintaining geometric constraints, the method improves topological quality without sacrificing the geometric precision produced by automatic generators.
2Manufacturing precision
If mesh improvement and refinement techniques are applied, then geometric quality is maintained, but control over topological quality remains very limited
Solution Approach 1:
The algorithm provides feedback control over topological quality by counting singularities in each patch and applying reduction operations when singularity counts exceed thresholds. This systematic feedback mechanism gives precise control over topological quality while preserving the geometric quality improvements from mesh refinement techniques.
Solution Approach 2:
The mesh optimization process performs self-service by automatically identifying patches with excessive singularities and applying reduction operations without external intervention. This self-service capability provides direct control over topological quality while maintaining the geometric quality achieved through refinement.
3Reliability
If global optimization problems are formulated for quad and hex meshing, then both geometric and topological quality can be addressed, but computational expense increases and parametric tweaking becomes non-intuitive
Solution Approach 1:
The global optimization problem is segmented into local patch-level operations. Instead of optimizing the entire mesh globally, the algorithm processes individual patches independently, identifying and reducing singularities in each patch. This segmentation dramatically reduces computational expense while maintaining control over topological quality.
Solution Approach 2:
The invention applies local quality optimization by treating each patch independently with its own singularity count and reduction operations. This local approach allows intuitive control over topological quality in each region without the computational burden of global optimization, while still achieving overall mesh improvement.
4Productivity
If local operations are applied to refine or coarsen quad mesh, then efficiency is improved, but additional singularities are created
Solution Approach 1:
The invention converts the harmful effect of local operations creating singularities into a beneficial process by systematically identifying and reducing those singularities. Local refinement operations are permitted to提高效率, and then singularity reduction operations are applied to eliminate the harmful side effect, turning the creation of singularities into an opportunity for targeted topological optimization.
Data Source
AI summary
Systems and methods for modifying and generating quadrilateral meshes for computer graphic structures include obtaining a polygon mesh representing a computer graphic structure, the polygon mesh comprising a plurality of polygonal faces and a plurality of singularities, determining, based on a first singularity of the plurality of vertices, selecting, based on one or more characteristics of the patch, a first minimum singularity template (MST) of a plurality of MSTs each representing a corresponding quadmesh that has three or fewer singularities, and replacing, within the polygon mesh, the patch with the first MST.