Hybrid Variational 3D Mesh Smoothing for Concave Domain Stability
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Solution Overview
Problem
Current 3D mesh smoothing techniques, such as Laplacian smoothing and optimization-based methods, fail to produce stable meshes in concave domains and often result in inverted or invalid elements, lacking user control and flexibility, especially when dealing with legacy FEM data.
Innovation Solution
A hybrid, variational, user-controlled 3D mesh smoothing approach that combines energy and equi-potential minimization theories, employing different smoothing techniques based on nodal valency and element connectivity to minimize element included angles and skewness, ensuring stability and quality while preserving mapped meshes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If Laplacian smoothing is used, then the smoothing process is simple and fast, but it produces inverted or invalid elements in concave domains and lacks user control
Solution Approach 1:
The patent applies different smoothing strategies to different regions of the mesh based on local characteristics. It identifies concave domains versus convex regions and applies appropriate smoothing methods to each, ensuring mesh stability in concave areas while maintaining speed in convex regions. This local differentiation resolves the contradiction between simple fast smoothing and reliable stable mesh production.
Solution Approach 2:
The patent implements a dynamic smoothing approach where the smoothing algorithm adapts based on user input and mesh characteristics. Users can control smoothing parameters and select different smoothing types (Laplacian, optimization-based, or hybrid) based on the specific problem requirements. This dynamic adaptability allows the system to maintain both speed and reliability by switching strategies as needed.
2Manufacturing precision
If optimization-based smoothing is used, then mesh quality is improved, but computational time increases significantly (5-40 times slower)
Solution Approach 1:
The patent segments the mesh into different regions (concave domains, convex regions, mapped meshes) and applies appropriate smoothing methods to each segment. This segmentation allows the system to use fast Laplacian smoothing for convex regions while reserving optimization-based methods for problematic concave regions, thereby maintaining overall efficiency while improving mesh quality where needed.
Solution Approach 2:
The patent merges multiple smoothing techniques into a unified hybrid approach. It combines the speed of Laplacian smoothing with the quality improvement of optimization-based methods and the geometric accuracy of mapped mesh preservation techniques. This merging creates a comprehensive smoothing system that achieves both high mesh quality and acceptable computational efficiency.
3Manufacturing precision
If smart Laplacian methods are used, then element distortion is reduced, but they still fail to produce stable meshes in concave domains
Solution Approach 1:
The patent detects concave domains by analyzing element geometry and reverses the smoothing approach for these regions. Instead of applying standard Laplacian smoothing that pushes nodes outward, it uses specialized algorithms that constrain nodes within concave boundaries or applies inverse operations to correct distorted elements. This inverted approach resolves the instability issue in concave domains while maintaining distortion control.
Solution Approach 2:
The patent implements feedback mechanisms that continuously monitor mesh quality parameters (element angles, skewness, Jacobian determinants) during the smoothing process. When concave domains are detected or element distortion exceeds thresholds, the algorithm automatically adjusts its behavior by switching to alternative smoothing strategies or applying corrective operations. This feedback control ensures mesh stability while maintaining precision.
4Manufacturing precision
If mapped meshes are preserved, then geometric accuracy is maintained, but existing smoothing techniques fail to recognize and preserve them
Solution Approach 1:
The patent changes the approach parameters based on mesh type detection. It identifies mapped meshes by analyzing node connectivity patterns and coordinate relationships, then switches to specialized smoothing algorithms that preserve the mapped structure. This parameter adaptation allows the system to maintain geometric accuracy in mapped regions while handling other mesh types with appropriate algorithms, thereby improving overall versatility.
Data Source
AI summary
A system and method for a hybrid, variational, user-controlled, 3D mesh smoothing for orphaned shell meshes. The smoothing model is based on a variational combination of energy and equi-potential minimization theories. A variety of smoothing techniques for predicting a new location for the node-to-smooth are employed. Each node is moved according to a specific smoothing algorithm so as to keep element included angles, skew and distortion to a minimum. The variational smoother selection logic is based on nodal valency and element connectivity pattern of the node to smooth. Results show its consistency with both quadrilateral and quad-dominant meshes with a significant gain over conventional Laplacian schemes in terms of mesh quality, stability, user control and flexibility.