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Quality meshing for polyhedra with small angles

Siu-Wing Cheng, Tamal K. Dey, Edgar A. Ramos, Tathagata Ray
2004 Proceedings of the twentieth annual symposium on Computational geometry - SCG '04  
We present an algorithm to compute a Delaunay mesh conforming to a polyhedron possibly with small input angles.  ...  Our experimental results validate that few skinny tetrahedra remain and they lie close to small acute input angles.  ...  Acknowledgments We thank the anonymous referees for their detailed and helpful comments.  ... 
doi:10.1145/997817.997862 dblp:conf/compgeom/ChengDRR04a fatcat:yfwtqupwhjawvmvwo6k4rvybiu

All-Hex Meshing of Multiple-Region Domains without Cleanup

Muhammad A. Awad, Ahmad A. Rushdi, Misarah A. Abbas, Scott A. Mitchell, Ahmed H. Mahmoud, Chandrajit L. Bajaj, Mohamed S. Ebeida
2016 Procedia Engineering  
In this paper, we present a new algorithm for all-hex meshing of domains with multiple regions without post-processing cleanup. Our method starts with a strongly balanced octree.  ...  Then we intersect the moved grid with the geometry. This allows us to avoid creating any flat angles, and we are able to handle two-sided regions and more complex topologies than prior methods.  ...  To get good quality hexes, it is sufficient to have cells and facets with modest aspect ratios, and bounded minimum to maximum edge lengths, and bounded dihedral and edge-angles; the resulting quality  ... 
doi:10.1016/j.proeng.2016.11.055 pmid:28845204 pmcid:PMC5568131 fatcat:py374n2g35gchpm7kq6anhqzgm

Adaptive and quality tetrahedral mesh generation

Jun Wang, Zeyun Yu
2011 2011 IEEE International Conference on Computer Science and Automation Engineering  
The quality of the tetrahedral meshes obtained is measured by dihedral angles, which are greater than 6° in all the models we have tested.  ...  This short paper presents an algorithm to generate adaptive and quality tetrahedral meshes from an arbitrary surface mesh model.  ...  The original marching tetrahedra algorithm is able to produce smooth triangular meshes but very small angles are often encountered.  ... 
doi:10.1109/csae.2011.5952690 fatcat:ngsohqxr4nc7jb34ewb7strevy

Advances in Octree-Based All-Hexahedral Mesh Generation: Handling Sharp Features [chapter]

Loïc Maréchal
2009 Proceedings of the 18th International Meshing Roundtable  
This paper presents advances made in the Hexotic project, especially in terms of sharp angles meshing, non-manifold geometries and adaptation.  ...  Even though many methods have been suggested to meet the challenge of all-hexahedral meshing, octree-based methods remain the most efficient from an engineering point of view.  ...  Meshing small features (shell or beam-shaped) with two hexes across allows for much less element distortion in the final boundary recovery process.  ... 
doi:10.1007/978-3-642-04319-2_5 dblp:conf/imr/Marechal09 fatcat:jltwqzn3ureojnzzxowcf4hscy

Lattice Cleaving: Conforming Tetrahedral Meshes of Multimaterial Domains with Bounded Quality [chapter]

Jonathan R. Bronson, Joshua A. Levine, Ross T. Whitaker
2013 Proceedings of the 21st International Meshing Roundtable  
The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity.  ...  We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials.  ...  This work was supported in part by grants from the US National Institutes of Health/National Center for Research Resources Center for Integrative Biomedical Computing, 2P41 RR01125523-12.  ... 
doi:10.1007/978-3-642-33573-0_12 pmid:25309969 pmcid:PMC4190882 dblp:conf/imr/BronsonLW12 fatcat:6ncj5zfpuzfqhgnmudlvx5r7wq

Feature-sensitive tetrahedral mesh generation with guaranteed quality

Jun Wang, Zeyun Yu
2012 Computer-Aided Design  
Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°.  ...  This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model.  ...  With our approach, however, there is no quality requirement for the input surface mesh.  ... 
doi:10.1016/j.cad.2012.01.002 pmid:22328787 pmcid:PMC3275789 fatcat:zyetiray5zafbciohx26a4kfza

Unstructured Mesh Generation [chapter]

Jonathan Shewchuk
2012 Combinatorial Scientific Computing  
The second constraint forbids small angles, albeit not for all applications.  ...  Polygonal domains with small angles can be meshed by cutting off the sharp corners before applying a standard meshing algorithm to the remainder [11] .  ...  The problem of domains with small angles is solved for triangular meshes by a remarkably elegant tweak by Miller, Pav, and Walkington [81] that perfects Ruppert's algorithm.  ... 
doi:10.1201/b11644-11 fatcat:zjfel6436jhwlidqrtkvjt3ezy

Polyhedrization of an arbitrary 3D point set

Sergio R. Idelsohn, Nestor Calvo, Eugenio Oñate
2003 Computer Methods in Applied Mechanics and Engineering  
The domain partition into polyhedra presented here is not a standard mesh generation.  ...  Nowadays, there are several acceptable shape functions for a very large class of polyhedra.  ...  Thanks are also given to Adri a an Cisilino and Gerardo Mazzetta for providing the data for the dinosaur example.  ... 
doi:10.1016/s0045-7825(03)00298-6 fatcat:ffr4z7qk2rfw7gtheapfsdfp7q

Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees

Jonathan Bronson, Joshua A. Levine, Ross Whitaker
2014 IEEE Transactions on Visualization and Computer Graphics  
The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity.  ...  We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials.  ...  ACKNOWLEDGMENTS Thanks to Adam Bargteil and Darrell Swenson for the simulation and experiment data sets.  ... 
doi:10.1109/tvcg.2013.115 pmid:24356365 pmcid:PMC4142801 fatcat:pdm2af6m6fdrnp2vtyz6ny6dhu

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1992 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  But if Q e is reversed, we remove e from the triangulation, replacing it with the other diagonal of Q e .  ...  Conclusions We have described work in computational geometry motivated by nite element mesh generation.  ... 
doi:10.1142/9789814355858_0002 fatcat:zjlfgakee5df7nihosmpeuhco4

MESH GENERATION AND OPTIMAL TRIANGULATION [chapter]

MARSHALL BERN, DAVID EPPSTEIN
1995 Lecture Notes Series on Computing  
We discuss algorithms both for the optimization of triangulations on a xed set of vertices and for the placement of new vertices (Steiner points).  ...  But if Q e is reversed, we remove e from the triangulation, replacing it with the other diagonal of Q e .  ...  Conclusions We have described work in computational geometry motivated by nite element mesh generation.  ... 
doi:10.1142/9789812831699_0003 fatcat:ec6436f5i5bszheuiherz452ae

Interactive Deformation of 3D Mesh Models

Hiroshi Masuda, Kenta Ogawa
2008 Computer-Aided Design and Applications  
the rotation of constraints for 3D meshes.  ...  This research has shown that 3D mesh models can be deformed in an interactive manner and with a practical amount of preprocessing time.  ...  Fig. 9 : 9 Quality of a deformed mesh with a large fixed region. Fig. 10 : 10 Mesh quality of rotated mesh. (a) Original; (b) partly-severed model; (c) deformed model with 3D texture.  ... 
doi:10.3722/cadaps.2008.47-57 fatcat:erxqbuquargzfprtnohmry2fuy

Virtual elements on agglomerated finite elements to increase the critical time step in elastodynamic simulations [article]

N. Sukumar, Michael R. Tupek
2022 arXiv   pre-print
For a suite of illustrative finite element meshes with ϵ being a mesh-coordinate parameter that leads to poor mesh quality, we show that adopting VEM on the agglomerated polyhedra yield critical time steps  ...  For reliable simulations on such meshes, we consider FE meshes with tetrahedral and prismatic elements that have badly-shaped elements-tetrahedra with dihedral angles close to 0^∘ and 180^∘, and slender  ...  Helpful discussions with Franco Dassi are also gratefully acknowledged.  ... 
arXiv:2110.00514v2 fatcat:monalcneebb4ddm7pu4pvaw66y

The extended Delaunay tessellation

Nestor Calvo, Sergio R. Idelsohn, Eugenio Oñate
2003 Engineering computations  
Nowadays, there are several acceptable shape functions for a very large class of polyhedra.  ...  Until recently, all the FEM mesh generators were limited to the generation of tetrahedral or hexahedral elements (or triangular and quadrangular in 2D problems).  ...  Classical definition of mesh quality will not be used here.  ... 
doi:10.1108/02644400310488763 fatcat:awozuipt3jg4ppymtyzhjloiya

Efficient and Global Optimization-Based Smoothing Methods for Mixed-Volume Meshes [chapter]

Dimitris Vartziotis, Benjamin Himpel
2014 Proceedings of the 22nd International Meshing Roundtable  
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes.  ...  We also identify some algorithms based on simple regularizing geometric element transformation optimizing certain global algebraic mesh quality measures.  ...  translationinvariant quality measure q e for polyhedra, which is essentially maximized by regular polyhedra [29] .  ... 
doi:10.1007/978-3-319-02335-9_17 dblp:conf/imr/VartziotisH13 fatcat:gb2iktsqubgjxhycxanyo3fn2m
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