An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg--Landau Theory

DOI10.1137/17M1142703zbMath1410.35223arXiv1708.02316OpenAlexW2963145016WikidataQ128491355 ScholiaQ128491355MaRDI QIDQ4623139

Ryan Viertel, Braxton Osting

Publication date: 19 February 2019

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.02316

zbMATH Keywords

computational geometryGinzburg-Landau theorygeometry processingquad meshing\(N\)-direction fieldscross fields

Mathematics Subject Classification ID

Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Ginzburg-Landau equations (35Q56)

Related Items (17)

Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains ⋮ Diffusion generated methods for denoising target-valued images ⋮ Quadrilateral mesh generation. II: Meromorphic quartic differentials and Abel-Jacobi condition ⋮ Tetrahedral frame fields via constrained third-order symmetric tensors ⋮ An unconditionally stable threshold dynamics method for the Willmore flow ⋮ Feature-aware reconstruction of trimmed splines using Ricci flow with metric optimization ⋮ Why cross fields are not equivalent to quadrilateral meshes ⋮ The quad layout immersion: a mathematically equivalent representation of a surface quadrilateral layout ⋮ An improved threshold dynamics method for wetting dynamics ⋮ A high resolution PDE approach to quadrilateral mesh generation ⋮ Quadrilateral mesh generation. III: Optimizing singularity configuration based on Abel-Jacobi theory ⋮ A diffusion generated method for orthogonal matrix-valued fields ⋮ A Variational Method for Generating $n$-Cross Fields Using Higher-Order $Q$-Tensors ⋮ Interface Dynamics for an Allen--Cahn-Type Equation Governing a Matrix-Valued Field ⋮ Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold ⋮ Anisotropic mesh generation and adaptation for quads using the \(L_p\)-CVT method ⋮ Global Parametrization Based on Ginzburg-Landau Functional

Uses Software

• CUBIT
• ALGLIB
• QuadCover

Cites Work

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