Finding hexahedrizations for small quadrangulations of the sphere

Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean‐François

doi:10.1145/3306346.3323017

Cited by 10 publications

(5 citation statements)

References 52 publications

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“…This local meshing step is highly critical, because of both topological [Mit96, Thu93, Eri13] and algorithmic constraints that often prevent the meshing of a sub‐volume, even with simple geometry. In particular, mesh conformity is typically enforced by first producing a quad tessellation of the shared interfaces and then filling the interior of each cavity with hexahedra using a direct meshing strategy [LW08, MH99, TBM96, VPR19,Mit99,CSS06,KBLK14]. However, direct methods are often heuristic and/or computationally expensive, making it hard for the software to assist the user even in basic tasks, such as recognizing whether a given decomposition is already meshable or guiding early decisions during the decomposition.…”

Section: Related Workmentioning

confidence: 99%

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%

HexBox: Interactive Box Modeling of Hexahedral Meshes

Zoccheddu,

Gobbetti,

Livesu

et al. 2023

Computer Graphics Forum

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“…If the branches are composed of a single extruded hex, we are left with a set of incoming quads around branching points. Filling the polyhedron formed by these quads with hexahedra is a very complicated problem in the general case [VPR19]. To address this issue, an alternative approach is proposed in [VKB21].…”

Section: Algorithm Detailsmentioning

confidence: 99%

Meso‐Skeleton Guided Hexahedral Mesh Design

Viville,

Kraemer,

Bechmann

2023

Computer Graphics Forum

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We present a novel approach for the generation of hexahedral meshes in a volume domain given its meso‐skeleton. This compact representation of the topology and geometry, composed of both curve and surface parts, is used to produce a raw decomposition of the domain into hexahedral blocks. Analysis of the different local configurations of the skeleton leads to the construction of a set of connection surfaces that are used as a scaffold onto which the hexahedral blocks are assembled. These local configurations of the skeleton completely determine the singularities of the final mesh, and by following the skeleton, the geometry of the produced mesh naturally follows the geometry of the domain. Depending on the end user needs, the obtained mesh can be further adapted, refined or optimized, for example to better fit the boundary of the domain. Our algorithm does not involve the resolution of any global problem, most decisions are taken locally and it is thus highly suitable for parallel processing. This efficiency allows the user to stay in the loop for the correction or edition of the meso‐skeleton for which a first sketch can be given by an existing automatic extraction algorithm.

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“…24, it provides geometric realizations with a maximum number of 72 hexahedra, thus proving that it is possible to mesh any ball-shaped domain that is bounded by 𝑛 quadrangles with a maximum number of 78𝑛 hexahedra. Image from [Verhetsel et al 2019b].…”

Section: Flipping Operatorsmentioning

confidence: 99%

“…(bottom) Cells with 22 quadrilaterals are meshed with 40 hexahedra. Elements are colour codeded to show the different sides of the original cubes (top-left and bottom-left).Image from[Verhetsel et al 2019b].…”

mentioning

confidence: 99%