Research Paper#Computational Geometry, Mesh Generation, Isogeometric Analysis🔬 ResearchAnalyzed: Jan 4, 2026 00:20
Regularity Analysis and Verification of Coons Volume Mappings
Analysis
This paper addresses a critical issue in 3D parametric modeling: ensuring the regularity of Coons volumes. The authors develop a systematic framework for analyzing and verifying the regularity, which is crucial for mesh quality and numerical stability. The paper's contribution lies in providing a general sufficient condition, a Bézier-coefficient-based criterion, and a subdivision-based necessary condition. The efficient verification algorithm and its extension to B-spline volumes are significant advancements.
Key Takeaways
- •Develops a systematic framework for analyzing and verifying the regularity of Coons volumes.
- •Introduces a criterion based on Bézier coefficients for efficient verification.
- •Provides a subdivision strategy combined with Bézier blossoming for ensuring regularity.
- •The method is extended to multi-patch B-spline volumes.
- •The algorithm enables real-time application due to its speed.
Reference
“The paper introduces a criterion based on the Bézier coefficients of the Jacobian determinant, transforming the verification problem into checking the positivity of control coefficients.”