Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

Ruiz‐Gironés, Eloi; Roca, Xevi; Sarrate, Josep; Montenegro, R.; Escobar, J. M.

doi:10.1016/j.advengsoft.2014.09.021

Cited by 29 publications

(10 citation statements)

References 36 publications

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“…While these inverted elements are not a problem for solving Poisson problems, it prevents using these meshes for other PDEs like non‐linear elasticity. This is a limitation shared with most recent hexahedral meshing and improvement methods [Knu00, Knu03, BDK*03, Mar09, GSZ11, NRP11, HTWB11, LLX*12, WSRRR*12, JHW*14, LVS*13, HJS*14, RGRS14, RGRS*15, LSVT15, GMD*16, GDC15, LMPS16, Mar16, FXBH16, FBL16, LBK16, GPW*17, CAS*19] and we believe is an important direction to find a way to integrate conservative inversion checks such as [Zha19] into a mesh optimization framework.…”

Section: Discussionmentioning

confidence: 99%

“…The topological complexity can also be reduced using local operations [BLK11, TPP*11, MPKZ10, GDC15, GPW*17]. The geometrical quality of a hex‐mesh can also be improved relocating its nodes without changing their connectivity [Knu00, Knu03, BDK*03, WSRRR*12, RGRS14, RGRS*15, LSVT15, XGC18]. All these methods are orthogonal to our contribution and could be used to postprocessing our meshes for specific applications.…”

Section: Related Workmentioning

confidence: 99%

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Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Computer Graphics Forum

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We propose an octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user‐controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self‐intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly‐lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open‐source implementation will be made available online to foster further research in this direction.

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Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Computer Graphics Forum

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“…Then, we define the objective function as

f false(boldx false) = true \sum_{j = 1}^{m} η_{E_{j}} false(bold-italicJ bold-italicϕ false),

where E j is the j th element adjacent to the node. The derivatives of the objective function are evaluated analytically according to Ruiz‐Gironés et al…”

Section: Surface Insertion Algorithmmentioning

confidence: 99%

“…where E j is the jth element adjacent to the node. The derivatives of the objective function are evaluated analytically according to Ruiz-Gironés et al 32…”

Section: Objective Functionmentioning

confidence: 99%

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Ruiz‐Gironés

Oliver

Socorro-Marrero

et al. 2017

Numerical Meth Engineering

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This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.Peer ReviewedPostprint (author's final draft

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“…However, these methods suffer from several drawbacks: they tend to produce unnecessarily high resolution meshes, they are not invariant to rotation (i.e., the same volume can be meshed differently, when rotated) and they tend to push the elements of worst quality near the boundary. Our method is rotationally invariant and generates boundary conforming hexmeshes (Figure ) with much less elements, also promoting high quality hexahedra near the boundary, an important requirement to ensure accurate simulations [RGRS*15].…”

Section: Related Workmentioning

confidence: 99%

Skeleton‐driven Adaptive Hexahedral Meshing of Tubular Shapes

Livesu

Muntoni

Puppo

et al. 2016

Computer Graphics Forum

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We propose a novel method for the automatic generation of structured hexahedral meshes of articulated 3D shapes. We recast the complex problem of generating the connectivity of a hexahedral mesh of a general shape into the simpler problem of generating the connectivity of a tubular structure derived from its curve-skeleton. We also provide volumetric subdivision schemes to nicely adapt the topology of the mesh to the local thickness of tubes, while regularizing per-element size. Our method is fast, one-click, easy to reproduce, and it generates structured meshes that better align to the branching structure of the input shape if compared to previous methods for hexa mesh generation

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Simultaneous untangling and smoothing of quadrilateral and hexahedral meshes using an object-oriented framework

Cited by 29 publications

References 36 publications

Feature Preserving Octree‐Based Hexahedral Meshing

Feature Preserving Octree‐Based Hexahedral Meshing

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Skeleton‐driven Adaptive Hexahedral Meshing of Tubular Shapes

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