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Algebraic Representations for Volumetric Frame Fields [article]

David Palmer Massachusetts Institute of Technology
2019 arXiv   pre-print
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct  ...  , better capturing the singular behavior we expect to see in volumetric frame fields.  ...  We thank Heng Liu for providing tetrahedral refinement, parametrization, and hexahedral mesh extraction code.  ... 
arXiv:1908.05411v1 fatcat:tksosgkw3fe55g576gyx423jge

Algebraic Representations for Volumetric Frame Fields

David Palmer, David Bommes, Justin Solomon
2020 ACM Transactions on Graphics  
Field-guided parameterization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct  ...  , better capturing the singular behavior we expect to see in volumetric frame fields.  ...  We thank Heng Liu for providing tetrahedral refinement, parameterization, and hexahedral mesh extraction code.  ... 
doi:10.1145/3366786 fatcat:2oki2km6pfbczdtrpi275hiwm4

Frame Field Singularity Correctionfor Automatic Hexahedralization

Tengfei Jiang, Jin Huang, Yuanzhen Wang, Yiying Tong, Hujun Bao
2014 IEEE Transactions on Visualization and Computer Graphics  
Such singularities could be abundant in automatically generated frame fields guiding the interior and boundary layouts of the hexahedra in an all hexahedral mesh.  ...  We then give a practical framework for adjusting singularity graphs by automatically modifying the rotational transition of frames between charts (cells of a tetrahedral mesh for the volume) to resolve  ...  However, there is no existing work on automatic surface singularity and internal singularity adjustment for frame fields used in hexahedral meshing, except a concurrent work on hexahedral meshing by Li  ... 
doi:10.1109/tvcg.2013.250 pmid:26357370 fatcat:3piwnd6vqndyde6hmmfju5b3le

Hex-Mesh Generation and Processing: a Survey [article]

Nico Pietroni, Marcel Campen, Alla Sheffer, Gianmarco Cherchi, David Bommes, Xifeng Gao, Riccardo Scateni, Franck Ledoux, Jean-Francois Remacle, Marco Livesu
2022 arXiv   pre-print
In this article, we provide a detailed survey of techniques for hexahedral mesh generation.  ...  We cover the whole spectrum of alternative approaches to mesh generation, as well as post processing algorithms for connectivity editing and mesh optimization.  ...  Besides providing directional guidance for hexahedral mesh elements, a key property of a frame field is its network of singularities -which one commonly aims to adopt for a hexahedral mesh generated based  ... 
arXiv:2202.12670v1 fatcat:ze2zfkgxhrgjnp2jm77wvgwvim

Multiple Approaches to Frame Field Correction for CAD Models

Maxence Reberol, Alexandre Chemin, Jean-François Remacle
2020 Zenodo  
Three-dimensional frame fields computed on CAD models often contain singular curves that are not compatible with hexahedral meshing.  ...  We eventually recommend the 3-5 singular curve boundary snapping strategy, which is simple to implement and allows to generate topologically correct frame fields.  ...  It allows additional singular curves that make the frame field singularity graph valid for hexahedral meshing.  ... 
doi:10.5281/zenodo.3653414 fatcat:5dfzf5lupvhezomnde2spwi46q

Multiple Approaches to Frame Field Correction for CAD Models [article]

Maxence Reberol, Alexandre Chemin, Jean-Francois Remacle
2019 arXiv   pre-print
Three-dimensional frame fields computed on CAD models often contain singular curves that are not compatible with hexahedral meshing.  ...  We eventually recommend the 3-5 singular curve boundary snapping strategy, which is simple to implement and allows to generate topologically correct frame fields.  ...  It allows additional singular curves that make the frame field singularity graph valid for hexahedral meshing.  ... 
arXiv:1912.01248v2 fatcat:fjyjexzwbzfsvhejjpqbvcggri

Frame Field Operators [article]

David R. Palmer
2021 arXiv   pre-print
The anisotropy is parametrized by a symmetric frame field, first studied in connection with quadrilateral and hexahedral meshing, which allows for fine-grained control of local directions of variation.  ...  Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing.  ...  Acknowledgments The authors would like to thank Mirela Ben-Chen and David Bommes for their thoughtful insights and feedback, as well as Xianzhong Fang and Jin Huang for helping with some speculative experiments  ... 
arXiv:2106.14360v1 fatcat:pi3zcvtdtndwdgdmeduzgwnezq

Octahedral Frames for Feature-Aligned Cross-Fields [article]

Paul Zhang, Josh Vekhter, Edward Chien, David Bommes, Etienne Vouga, Justin Solomon
2020 arXiv   pre-print
We demonstrate the applicability of our method to quad-meshing and include an extensive benchmark comparing our fields to other automatic approaches for generating feature-aligned cross fields on triangle  ...  meshes.  ...  ACKNOWLEDGMENTS The authors would like to thank Christopher Brandt for help obtaining comparison fields, Amir Vaxman for support with Directional and rendering, Michal Adamaszek for help debugging Mosek  ... 
arXiv:2007.09740v1 fatcat:zoyrcpvfqzhelm36unusi77gni

Octahedral Frames for Feature-Aligned Cross Fields

Paul Zhang, Josh Vekhter, Edward Chien, David Bommes, Etienne Vouga, Justin Solomon
2020 ACM Transactions on Graphics  
ACKNOWLEDGMENTS The authors would like to thank Christopher Brandt for help obtaining comparison fields, Amir Vaxman for support with Directional and rendering, Michal Adamaszek for help debugging Mosek  ...  We thank Wenzel Jacob, Keenan Crane, and Qingnan Zhou for their open source code implementations. Finally, we thank Ryan Viertel for many valuable discussions and Panini Pals for the panini press.  ...  SH functions have been used successfully in volumetric octahedral field problems for hexahedral meshing [Huang et al. 2011; Ray et al. 2016; Solomon et al. 2017 ], and we argue that this representation  ... 
doi:10.1145/3374209 fatcat:o2prsqx7nfduri6gzbcrpdvqge

A Large Scale Comparison of Tetrahedral and Hexahedral Elements for Finite Element Analysis [article]

Teseo Schneider, Yixin Hu, Xifeng Gao, Jeremie Dumas, Denis Zorin, Daniele Panozzo
2019 arXiv   pre-print
For all these cases, we use state-of-the-art meshing tools to create both unstructured (tetrahedral) and structured (hexahedral) meshes, and compare the performance of different element types for a wide  ...  This observation suggests that for most problems in static structural analysis, thermal analysis, and low reynolds number flows, it is unnecessary to target automatic hex mesh generation, since high-quality  ...  Bommes, Singularity-constrained octahedral fields for hexahedral meshing, ACM Transactions on Graphics 37 (4) (2018) 1–17. doi:10.1145/3197517. 3201344. [108] M. Bracci, M. Tarini, N.  ... 
arXiv:1903.09332v2 fatcat:ikoc2la6jrcufmo773zjl4jhpu

Symmetric moving frames

Etienne Corman, Keenan Crane
2019 ACM Transactions on Graphics  
frames can be naturally applied in the symmetric case, and how to incorporate constraints needed for hexahedral meshing, namely, adaptation to a network of singular curves which correspond to mesh edges  ...  Here, a valid network means one that is compatible with the global topology of some hexahedral mesh, as recently studied by Liu et al. [2018].  ...  ACKNOWLEDGMENTS Thanks to Heng Liu and David Bommes for help with parameterization and mesh extraction, and to the anonymous reviewers for useful feedback.  ... 
doi:10.1145/3306346.3323029 fatcat:6aygspaa35hijmqdcwhwde2mm4

At‐Most‐Hexa Meshes

Dennis R. Bukenberger, Marco Tarini, Hendrik P. A. Lensch
2021 Computer graphics forum (Print)  
In contrast to existing methods for (pure) hexahedral meshing, ours does not require an intermediate parameterization of other costly pre-computations and can start directly from surfaces or samples.  ...  We leverage a Lloyd relaxation process to exploit the synergistic effects of aligning an orientation field in a modified 3D Voronoi diagram using the L ∞ norm for cubical cells.  ...  Others describe constraints on the octahedral fields of existing hexmeshes to minimize singularities [LZC*18] which then qualify as 'meshable' input for further elaborate orientation field computations  ... 
doi:10.1111/cgf.14393 fatcat:tguuepiofjdmxjaq4w2dvowthe

Topology of Frame Field Design for Hex Meshing [article]

Piotr Beben
2020 arXiv   pre-print
In the past decade frame fields have emerged as a promising approach for generating hexahedral meshes for CFD and CAE applications.  ...  One important problem asks for construction of a boundary-aligned frame field with prescribed singularity constraints over a volume that corresponds to a valid hexahedral mesh.  ...  Another approach known as integer-grid maps [22] yields a hex mesh directly by pulling back a hexahedral grid back to align with a frame field.  ... 
arXiv:2011.05276v6 fatcat:njofu223rjh5riki2s7tw7zope

Visualization and Processing of Anisotropy in Imaging, Geometry, and Astronomy (Dagstuhl Seminar 18442)

Andrea Fuster, Evren Özarslan, Thomas Schultz, Eugene Zhang, Michael Wagner
2019 Dagstuhl Reports  
These disciplines share a need for modeling, processing, and visualizing anisotropic quantities, which poses interesting challenges to applied computer science.  ...  octahedral fields for hexahedral meshing", ACM Trans.  ...  Overview of Talks Quadrilateral and Hexahedral Mesh Generation Automatically generating quadrilateral and hexahedral meshes that smoothly align to freeform surfaces and offer a high amount of regularity  ... 
doi:10.4230/dagrep.8.10.148 dblp:journals/dagstuhl-reports/FusterO0Z18 fatcat:mlcgmrzo5fexfikbsmtpt5wwzy

A variational method for generating n-cross fields using higher-order Q-tensors [article]

Dmitry Golovaty, Jose Alberto Montero, Daniel Spirn
2020 arXiv   pre-print
Cross fields are finding wide-spread use in mesh generation, computer graphics, and materials science among many applications.  ...  Our approach is designed to fit within the classical Ginzburg-Landau PDE theory, offering a concrete road map for the future careful study of singularities of energy minimizers.  ...  The related recent work has been done on singularity-constrained octahedral fields for hexahedral meshing [21] , boundary element octahedral fields in volumes [30] , smoothness driven frame field generation  ... 
arXiv:1909.00922v3 fatcat:guhvelc3lfbs5oka3qsq5htfqq
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