Advanced Automatic Hexahedral Mesh Generation from Surface Quad Meshes

Kremer, Martin; Bommes, David; Lim, Isaak; Kobbelt, Leif

doi:10.1007/978-3-319-02335-9_9

Cited by 25 publications

(19 citation statements)

References 25 publications

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“…Although they are able to generate a dual mesh, they do not generate the primal mesh. Recently, the dual method presented in [130] has been extended to more complex geometries in [132].…”

Section: Dual Methodsmentioning

confidence: 99%

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Ramos¹,

Ruiz‐Gironés²,

Navarro³

2014

Comp. Tech. Rev.

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Discretization techniques such the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in applied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to generate. However, in many applications such as boundary layers in computational fluid dynamics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.

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“…Although they are able to generate a dual mesh, they do not generate the primal mesh. Recently, the dual method presented in [130] has been extended to more complex geometries in [132].…”

Section: Dual Methodsmentioning

confidence: 99%

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Ramos¹,

Ruiz‐Gironés²,

Navarro³

2014

Comp. Tech. Rev.

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“…While these polycube maps are of interest for volumetric mapping and meshing purposes [GSZ11, HJS*14, FXBH16], the restriction to the specific sub‐class of quad layouts that can result from such a map does not necessarily provide particular benefits for the surface case from an application perspective, and particularly not in terms of computational simplicity or robustness. A potential benefit could be the general absence of self‐intersecting dual loops from polycube surface layouts, for example, for volumetric meshing purposes [MH02, KBLK13].…”

Section: Restricted Layout Classesmentioning

confidence: 99%

Partitioning Surfaces Into Quadrilateral Patches: A Survey

Campen

2017

Computer Graphics Forum

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The efficient and practical representation and processing of geometrically or topologically complex shapes often demands a partitioning into simpler patches. Possibilities range from unstructured arrangements of arbitrarily shaped patches on the one end, to highly structured conforming networks of all‐quadrilateral patches on the other end of the spectrum. Due to its regularity, this latter extreme of conforming partitions with quadrilateral patches, called quad layouts, is most beneficial in many application scenarios, for instance enabling the use of tensor‐product representations based on splines or Bézier patches, grid‐based multi‐resolution techniques and discrete pixel‐based map representations. However, this type of partition is also most complicated to create due to the strict inherent structural restrictions. Traditionally often performed manually in a tedious and demanding process, research in computer graphics and geometry processing has led to a number of computer‐assisted, semi‐automatic, as well as fully automatic approaches to address this problem more efficiently. This survey provides a detailed discussion of this range of methods, treats their strengths and weaknesses and outlines open problems in this field of research.

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“…Different from the octree‐based method, Kremer et al . [KBLK14] introduced an automatic technique that generates hex‐meshes from valid surface quad meshes based on the concept of dual loops. Additional singularities may still be introduced during the construction of a valid hexahedral topology.…”

Section: Related Workmentioning

confidence: 99%

Hexahedral Meshing With Varying Element Sizes

Gao

Deng

et al. 2017

Computer Graphics Forum

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Hexahedral (or Hex‐) meshes are preferred in a number of scientific and engineering simulations and analyses due to their desired numerical properties. Recent state‐of‐the‐art techniques can generate high‐quality hex‐meshes. However, they typically produce hex‐meshes with uniform element sizes and thus may fail to preserve small‐scale features on the boundary surface. In this work, we present a new framework that enables users to generate hex‐meshes with varying element sizes so that small features will be filled with smaller and denser elements, while the transition from smaller elements to larger ones is smooth, compared to the octree‐based approach. This is achieved by first detecting regions of interest (ROIs) of small‐scale features. These ROIs are then magnified using the as‐rigid‐as‐possible deformation with either an automatically determined or a user‐specified scale factor. A hex‐mesh is then generated from the deformed mesh using existing approaches that produce hex‐meshes with uniform‐sized elements. This initial hex‐mesh is then mapped back to the original volume before magnification to adjust the element sizes in those ROIs. We have applied this framework to a variety of man‐made and natural models to demonstrate its effectiveness.

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Advanced Automatic Hexahedral Mesh Generation from Surface Quad Meshes

Cited by 25 publications

References 25 publications

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Partitioning Surfaces Into Quadrilateral Patches: A Survey

Hexahedral Meshing With Varying Element Sizes

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