Hex-Mesh Generation and Processing: A Survey

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

doi:10.1145/3554920

Cited by 26 publications

(19 citation statements)

References 278 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We have systematically presented the indicators for assessing the quality of the elements of a mesh, classifying them according to the type of the element and the criteria adopted. While there is a large literature for simplicial [Knu03, SEK*07] and quadrilateral elements [BLP*13b], increasing attention is on hexahedral meshes [PCS*22], and there is still a wide room for research on polytopal ones. Then, we discussed how these indicators can be used to derive global mesh indicators and optimize the mesh in a variety of applicative contexts.…”

Section: Discussionmentioning

confidence: 99%

“…In this sense, quality indicators can be provided by the number of T‐junctions, or the number of non‐standard elements (for instance, the number of non‐quad cells in a quad‐dominant mesh). The two above requirements can sometimes be loosened [MPKZ10], but such topological freedom is not unlimited and may be bounded by the specific application [PCS*22].…”

Section: Mesh Indicatorsmentioning

confidence: 99%

“…Among the others, we refer to the seminal work of Hoppe et al [HDD*93]. Similarly, the majority of volumetric meshing algorithms, employ a two‐step process [PCS*22]. The first step generates an initial mesh, which is expected to be dominated by well‐shaped elements, but often also contains some poorly‐shaped or even degenerate elements.…”

Section: Mesh Quality Optimizationmentioning

confidence: 99%

See 2 more Smart Citations

A Survey of Indicators for Mesh Quality Assessment

Sorgente

Biasotti

Manzini

et al. 2023

Computer Graphics Forum

View full text Add to dashboard Cite

We analyze the joint efforts made by the geometry processing and the numerical analysis communities in the last decades to define and measure the concept of “mesh quality”. Researchers have been striving to determine how, and how much, the accuracy of a numerical simulation or a scientific computation (e.g., rendering, printing, modeling operations) depends on the particular mesh adopted to model the problem, and which geometrical features of the mesh most influence the result. The goal was to produce a mesh with good geometrical properties and the lowest possible number of elements, able to produce results in a target range of accuracy. We overview the most common quality indicators, measures, or metrics that are currently used to evaluate the goodness of a discretization and drive mesh generation or mesh coarsening/refinement processes. We analyze a number of local and global indicators, defined over two‐ and three‐dimensional meshes with any type of elements, distinguishing between simplicial, quadrangular/hexahedral, and generic polytopal elements. We also discuss mesh optimization algorithms based on the above indicators and report common libraries for mesh analysis and quality‐driven mesh optimization.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Mesh Indicatorsmentioning

confidence: 99%

Section: Mesh Quality Optimizationmentioning

confidence: 99%

See 1 more Smart Citation

A Survey of Indicators for Mesh Quality Assessment

Sorgente

Biasotti

Manzini

et al. 2023

Computer Graphics Forum

View full text Add to dashboard Cite

show abstract

“…Despite extensive research, the lack of reliable and effective automatic methods for hexahedral meshing is a well established and well documented open scientific problem [PCS*22], up to the point that manually crafting hexahedral meshes can still be considered the industry standard [LQS17]. At the same time, interactive and semi‐interactive modeling of hexahedral meshes is notoriously a difficult problem, and modeling sessions are known to be tedious and time consuming among practitioners.…”

Section: Introductionmentioning

confidence: 99%

“…HexBox takes care of all the topological constraints that must be fulfilled, ensuring that at any time during modeling, the mesh contains only hexahedral elements. This also includes enforcing, on demand, mesh conformity around areas with different refinements, which we address by exploiting recent advancements in adaptive grid‐based meshing [PCS*22](§4.6). A direct manipulation user interface lets users perform modeling by applying operations to selected areas of the mesh, provide immediate feedback, and exploiting the data structures maintained during modeling to also implement undoing, redoing, and parameterized replication of actions, as well as preservation of history across editing sessions (Sec.…”

Section: Introductionmentioning

confidence: 99%

HexBox: Interactive Box Modeling of Hexahedral Meshes

Zoccheddu,

Gobbetti,

Livesu

et al. 2023

Computer Graphics Forum

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Block‐structured mesh generation from implicit geometries for cardiovascular applications

Bošnjak,

Fries

2023

Proc Appl Math and Mech

View full text Add to dashboard Cite

Generation of suitable meshes for patient‐specific vascular domains remains a major obstacle in the context of numerical simulations relying on the finite element method, as well as many similar methods. Herein, we discuss a skeleton‐based structured meshing approach, revolving around block‐structures. We rely on an implicitly represented surface, either via a signed distance function, or a convolution surface. The mesh generation using the aforementioned concepts is performed through the proper utilisation of transfinite maps. Application‐wise, we consider healthy blood vessels, and extensions required to tackle aortas afflicted by aortic dissection. The high quality of the resulting meshes is affirmed through common mesh quality metrics. Our approach features large flexibility in terms of spatial resolution, as well as mesh order.

show abstract

Hex-Mesh Generation and Processing: A Survey

Cited by 26 publications

References 278 publications

A Survey of Indicators for Mesh Quality Assessment

A Survey of Indicators for Mesh Quality Assessment

HexBox: Interactive Box Modeling of Hexahedral Meshes

Block‐structured mesh generation from implicit geometries for cardiovascular applications

Contact Info

Product

Resources

About