Quadrilateral and Hexahedral Element Meshes

Schneiders, Robert

doi:10.1201/9781420050349.ch21

Cited by 48 publications

(66 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Schneiders [98] surveys quadrilateral and hexahedral meshing far more deeply. Bern and Eppstein [8] survey triangulation algorithms that optimize many criteria not discussed here.…”

Section: Methods Of Mesh Generationmentioning

confidence: 99%

Unstructured Mesh Generation

Shewchuk¹

2012

Combinatorial Scientific Computing

View full text Add to dashboard Cite

“…Schneiders [98] surveys quadrilateral and hexahedral meshing far more deeply. Bern and Eppstein [8] survey triangulation algorithms that optimize many criteria not discussed here.…”

Section: Methods Of Mesh Generationmentioning

confidence: 99%

Unstructured Mesh Generation

Shewchuk¹

2012

Combinatorial Scientific Computing

View full text Add to dashboard Cite

“…Hanging nodes can lead to cracks and pinholes on the output mesh, and are also undesirable from the perspective of mesh quality-a mesh with hanging nodes is not well suited for further processing. Schneiders [1996] proposed two different approaches based on refinement templates to solve this problem. His 3-refinement templates, which in some cases subdivide a face into 9 sub-faces, tend to generate a large number of small faces.…”

Section: Avoiding Cracks and T-junctionsmentioning

confidence: 99%

“…We have carefully chosen a compact but intuitive data structure to maintain the subdivision mesh, and perform updates to this structure in a completely parallel fashion. We also present a data-parallel technique that uses templates given by Schneiders [1996] to completely avoid cracks by eliminating T-junctions in the subdivided mesh. We demonstrate the validity of our strategy by achieving real-time performance for several real-life models.…”

Section: Introductionmentioning

confidence: 99%

Parallel view-dependent tessellation of Catmull-Clark subdivision surfaces

Patney

Ebeida

Owens

2009

Proceedings of the Conference on High Performance Graphics 2009

View full text Add to dashboard Cite

Figure 1:We adaptively subdivide faces of a Catmull-Clark subdivision mesh until the screen-space geometric criterion is met. Using a parallel approach to the subdivision procedure, we are able to obtain interactive performance for complex real-life models. Moreover, we ensure that the subdivided mesh is free of cracks and T-junctions. AbstractWe present a strategy for performing view-adaptive, crack-free tessellation of Catmull-Clark subdivision surfaces entirely on programmable graphics hardware. Our scheme extends the concept of breadth-first subdivision, which up to this point has only been applied to parametric patches. While mesh representations designed for a CPU often involve pointer-based structures and irregular perelement storage, neither of these is well-suited to GPU execution. To solve this problem, we use a simple yet effective data structure for representing a subdivision mesh, and design a careful algorithm to update the mesh in a completely parallel manner. We demonstrate that in spite of the complexities of the subdivision procedure, real-time tessellation to pixel-sized primitives can be done.Our implementation does not rely on any approximation of the limit surface, and avoids both subdivision cracks and T-junctions in the subdivided mesh. Using the approach in this paper, we are able to perform real-time subdivision for several static as well as animated models. Rendering performance is scalable for increasingly complex models.

show abstract

“…One special case of cleanup in hexahedral meshes for the whisker weaving algorithm is presented in [31]. Schneiders [32] proposed algorithms and a series of templates for quad/hex element decomposition. A recursive subdivision algorithm was proposed for the refinement of hexahedral meshes [33].…”

Section: Previous Workmentioning

confidence: 99%

Adaptive and quality quadrilateral/hexahedral meshing from volumetric data

Zhang

Bajaj

2006

Computer Methods in Applied Mechanics and Engineering

207

158

View full text Add to dashboard Cite

This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.

show abstract

Quadrilateral and Hexahedral Element Meshes

Cited by 48 publications

References 14 publications

Unstructured Mesh Generation

Unstructured Mesh Generation

Parallel view-dependent tessellation of Catmull-Clark subdivision surfaces

Adaptive and quality quadrilateral/hexahedral meshing from volumetric data

Contact Info

Product

Resources

About