Semi-global Quad Mesh Structure Simplification via Separatrix Operations

Xu, Kaoji; Akram, Muhammad Naeem; Chen, Guoning

doi:10.1145/3410700.3425436

Cited by 4 publications

(1 citation statement)

References 13 publications

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“…Decimating quads. A first family of approaches reduces the number of singularities in a mesh through mesh simplification -see, e.g., [Daniels et al 2008[Daniels et al , 2009Tarini et al 2010Tarini et al , 2011Xu et al 2020]. These methods iteratively decrease the number of singularities by decimating an input quad mesh through local operations (e.g., quad collapse or doublet removal) and/or semi-global operations (e.g., (half-)polychord removal, separatrix split between pairs of 5singularities, or separatrix collapse between pairs of 3-singularities) that preserve boundary features.…”

Section: Related Workmentioning

confidence: 99%

Q-zip

Feng¹,

Tong

Desbrun

2021

ACM Trans. Graph.

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Singularity editing of a quadrangle mesh consists in shifting singularities around for either improving the quality of the mesh elements or canceling extraneous singularities, so as to increase mesh regularity. However, the particular structure of a quad mesh renders the exploration of allowable connectivity changes non-local and hard to automate. In this paper, we introduce a simple, principled, and general quad-mesh editing primitive with which pairs of arbitrarily distant singularities can be efficiently displaced around a mesh through a deterministic and reversible chain of local topological operations with a minimal footprint. Dubbed Q-zip as it acts as a zipper opening up and collapsing down quad strips, our practical mesh operator for singularity editing can be easily implemented via parallel transport of a reference compass between any two irregular vertices. Batches of Q-zips performed in parallel can then be used for efficient singularity editing. CCS Concepts: • Mathematics of computing → Mesh generation.

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Section: Related Workmentioning

confidence: 99%

Q-zip

Feng¹,

Tong

Desbrun

2021

ACM Trans. Graph.

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Quadrilateral surface mesh generation with improved quality by combination of triangles

Gao,

Xiao,

et al. 2024

Numerical Meth Engineering

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Quadrilateral mesh is preferred in numerical simulation compared with triangular mesh, but high‐quality and robust quadrilateral mesh generation for complex geometries remains a challenging problem. In this study, an enhanced indirect method by the combination of triangles is proposed for the generation of high‐quality quadrilateral mesh. It takes a triangular mesh as the input, and except that the number of elements needs to be even, the triangular mesh can be generated by the commonly used AFT method or Delaunay method. To ensure the quality of the combined quads, a local‐global triangular remeshing procedure is conducted first, and size gradation and vertex valence are focused in this step. Then, the well‐known Blossom algorithm is used to find the perfect matching triangles for combination. Finally, in order to reduce the number of unnecessary singularities, a connectivity optimization procedure is introduced to replace the irregular elements in local regions with regular elements and thus improve the overall quality of the combined quads. Numerical experiments on meshes in both 2D and 3D cases are presented to demonstrate the effectiveness of the proposed method.

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Structure simplification of planar quadrilateral meshes

Akram

Chen

2022

Computers & Graphics

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Semi-global Quad Mesh Structure Simplification via Separatrix Operations

Cited by 4 publications

References 13 publications

Q-zip

Q-zip

Quadrilateral surface mesh generation with improved quality by combination of triangles

Structure simplification of planar quadrilateral meshes

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