Octree-Based Hexahedral Mesh Generation

Schneiders, Robert

doi:10.1142/s021819590000022x

Cited by 54 publications

(22 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With such a limitation, the full power of mesh optimization cannot be unlocked [5]. The advent of tools such as paving [6], plastering [7], whisker weaving [8], medial axis and surface [9], embedded Voronoi graph [10] or grid-based methods [11][12][13] for unstructured quadrilateral and hexahedral mesh generation brought the need for a new crop of adaptation methods. Recombination of quadrilaterals from adapted triangles [14,15] and rectangular cell packing [16] are very attractive but extensions in three dimensions are yet to be developed.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, iterative local refinement methods using quadtrees in two dimensions can be extended in three dimensions using octrees but result in non-conformal elements with hanging nodes that cannot be treated by some solvers. Although all-quadrilateral transition templates to remove those hanging nodes are readily available for quadtrees [17], it is only recently that all-hexahedral transition patterns have been developed for octrees [12,13]. The directional refinement method of Schneiders uses an octree to insert conformal buffer layers in alternating x, y, and z directions [12].…”

Section: Introductionmentioning

confidence: 99%

“…Although all-quadrilateral transition templates to remove those hanging nodes are readily available for quadtrees [17], it is only recently that all-hexahedral transition patterns have been developed for octrees [12,13]. The directional refinement method of Schneiders uses an octree to insert conformal buffer layers in alternating x, y, and z directions [12]. The resulting mesh is all-hexahedral but the method must start from a balanced octree.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Automated refinement of conformal quadrilateral and hexahedral meshes

Tchon

Dompierre

sCamarero

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYConformal refinement using a shrink and connect strategy, known as pillowing or buffer insertion, contracts and reconnects contiguous elements of an all-quadrilateral or an all-hexahedral mesh in order to locally increase vertex density without introducing hanging nodes or non-cubical elements. Using layers as shrink sets, the present method automates the anisotropic refinement of such meshes according to a prescribed size map expressed as a Riemannian metric field. An anisotropic smoother further enhances vertex clustering to capture the features of the metric. Both two-and three-dimensional test cases with analytic control metrics confirm the feasibility of the present approach and explore strategies to minimize the trade-off between element shape quality and size conformity. Additional examples using discrete metric maps illustrate possible practical applications. Although local vertex removal and reconnection capabilities have yet to be developed, the present refinement method is a step towards an automated tool for conformal adaptation of all-quadrilateral and all-hexahedral meshes.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Automated refinement of conformal quadrilateral and hexahedral meshes

Tchon

Dompierre

sCamarero

2004

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…However, although it can improve both vertex density and element shape, smoothing is limited by a fixed mesh topology. Mesh refinement and coarsening, on the other hand, involve connectivity modifications [9,10,11,12]. The major issue with conformal refinement-coarsening is, however, that element shape quality cannot be maintained without a powerful local reconnection method and the coveted cubical flip operator is still only theoretical in three dimensions [13].…”

Section: Cubical Adaptationmentioning

confidence: 99%

Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

Tchon

Camarero

Proceedings of the 15th International Meshing Roundtable

View full text Add to dashboard Cite

Summary. The proposed quad-dominant mesh adaptation algorithm is based on simplicial optimization. It is driven by an anisotropic Riemannian metric and uses specialized local operators formulated in terms of an L ∞ instead of the usual L2 distance. Furthermore, the physically-based vertex relocation operator includes an alignment force to explicitly minimize the angular deviation of selected edges from the local eigenvectors of the target metric. Sets of contiguous edges can then be effectively interpreted as active tensor lines. Those lines are not only packed but also simultaneous networked together to form a layered rectangular simplicial mesh that requires little postprocessing to form a cubical-dominant one. Almost all-cubical meshes are possible if the target metric is compatible with such a decomposition and, although presently only two-dimensional tests were performed, a three-dimensional extension is feasible.

show abstract

“…The plastering method is similar to the advancing front approach with hexahedral elements. 39 The Whisker weaving algorithm 40 first constructs the spatial twist continuum (STC: dual of the hexahedral mesh). 41 The medial surface method 42 decomposes the volume in a set of medial surfaces.…”

Section: Volumetric Meshingmentioning

confidence: 99%

From MRI to anatomical simulation of the hip joint

Assassi

Charbonnier

Schmid

et al. 2008

Computer Animation & Virtual

View full text Add to dashboard Cite

This paper describes a methodology for the simulation of musculoskeletal disorders. Our clinical study is related to osteoarthritis (OA) of the hip, a pathogenesis possibly due to impingements. These bone collisions lead to abnormal joint mechanics which is characterized by contact pressure and stress distribution upon the joint cartilages. The proposed methodology combines different approaches from modeling to simulation. The simulation is based on patient-specific anatomical models, where acquisition modalities are noninvasive and flexible. Based on static magnetic resonance imaging (MRI) data, a discrete deformable models method is used for modeling the organs of the musculoskeletal system. Femoroacetabular movements are estimated using an optical motion capture system and are validated by a dynamic MRI analysis. To achieve accurate deformations, techniques to generate volumetric meshes are developed based on the medial axis (MA) information. Finally, a computationally efficient fast functional joint model is used to simulate the mechanical behavior of the soft tissues. The goal of such a simulation is to allow the investigation of the relevant contact and cartilages deformation under movement, which can be useful for diagnosis, pre-or post-operative planning and training. This will benefit further developments in surgical techniques and minimally invasive procedures.

show abstract

Octree-Based Hexahedral Mesh Generation

Cited by 54 publications

References 5 publications

Automated refinement of conformal quadrilateral and hexahedral meshes

Automated refinement of conformal quadrilateral and hexahedral meshes

Quad-Dominant Mesh Adaptation Using Specialized Simplicial Optimization

From MRI to anatomical simulation of the hip joint

Contact Info

Product

Resources

About