A Course on Hex-Mesh Generation and Processing

Pietroni, Nico; Campen, Marcel; Sheffer, Alla; Cherchi, Gianmarco; Bommes, David; Gao, Xifeng; Scateni, Riccardo; Ledoux, Franck; Remacle, Jean-François; Livesu, Marco

doi:10.1145/3550495.3558207

Cited by 5 publications

(3 citation statements)

References 250 publications

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“…In the following, we only focus on the methods most closely related to ours, organizing them into methods that are fully automatic and methods that enjoy some form of user interaction, both in the industry and in academia. We refer the reader to a recent survey [PCS*22] and associated SIGGRAPH course [PCS*23] for a broader perspective.…”

Section: Related Workmentioning

confidence: 99%

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HexBox: Interactive Box Modeling of Hexahedral Meshes

Zoccheddu,

Gobbetti,

Livesu

et al. 2023

Computer Graphics Forum

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We introduce HexBox, an intuitive modeling method and interactive tool for creating and editing hexahedral meshes. Hexbox brings the major and widely validated surface modeling paradigm of surface box modeling into the world of hex meshing. The main idea is to allow the user to box‐model a volumetric mesh by primarily modifying its surface through a set of topological and geometric operations. We support, in particular, local and global subdivision, various instantiations of extrusion, removal, and cloning of elements, the creation of non‐conformal or conformal grids, as well as shape modifications through vertex positioning, including manual editing, automatic smoothing, or, eventually, projection on an externally‐provided target surface. At the core of the efficient implementation of the method is the coherent maintenance, at all steps, of two parallel data structures: a hexahedral mesh representing the topology and geometry of the currently modeled shape, and a directed acyclic graph that connects operation nodes to the affected mesh hexahedra. Operations are realized by exploiting recent advancements in grid‐based meshing, such as mixing of 3‐refinement, 2‐refinement, and face‐refinement, and using templated topological bridges to enforce on‐the‐fly mesh conformity across pairs of adjacent elements. A direct manipulation user interface lets users control all operations. The effectiveness of our tool, released as open source to the community, is demonstrated by modeling several complex shapes hard to realize with competing tools and techniques.

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Section: Related Workmentioning

confidence: 99%

“…Suppression of hanging nodes was mostly studied in the context of adaptive grid‐based hexmeshing [PCS*23](§4.6), where conformity must be restored locally, without affecting the whole mesh (Fig. 4, middle).…”

Section: Anatomy Of Hexboxmentioning

confidence: 99%

HexBox: Interactive Box Modeling of Hexahedral Meshes

Zoccheddu,

Gobbetti,

Livesu

et al. 2023

Computer Graphics Forum

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“…In other words, every element must be fully invertible. However, generating high-quality, tangle-free meshes remains a challenge, despite advances in mesh generation methods [5,6]. State-of-the-art mesh generation methods [7,8,9,10,11,12,13,14] can still lead to a tangled mesh.…”

Section: Introductionmentioning

confidence: 99%

Isoparametric Tangled Finite Element Method for Nonlinear Elasticity

Prabhune¹,

Suresh²

2023

Preprint

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An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric tangled finite element method (i-TFEM) was recently proposed for linear elasticity problems. It was demonstrated that i-TFEM leads to optimal convergence even for severely tangled meshes.In this paper, i-TFEM is generalized to nonlinear elasticity. Specifically, a variational formulation is proposed that leads to local modification in the tangent stiffness matrix associated with tangled elements, and an additional piece-wise compatibility constraint. i-TFEM reduces to standard FEM for tangle-free meshes. The effectiveness and convergence characteristics of i-TFEM are demonstrated through a series of numerical experiments, involving both compressible and in-compressible problems.

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