Robust structure simplification for hex re-meshing

Gao, Xifeng; Panozzo, Daniele; Wang, Wenping; Deng, Zhigang; Chen, Guoning

doi:10.1145/3130800.3130848

Cited by 37 publications

(54 citation statements)

References 44 publications

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“…We believe that our technique will have a large impact in the research community, since it will allow to automatically generate hundreds of coarse, feature‐preserving hexahedral meshes, providing a complete pipeline for generating IsoGeometric Aanalysis preferable hex‐meshes by coupling it with [GPW*17], opening the door to black‐box finite element analysis pipelines on hexa‐hedral meshes and allowing statistically significant comparisons between different types of meshes in graphics and engineering applications [SHG*19].…”

Section: Discussionmentioning

confidence: 99%

“…Distortion Energy Term. To measure the distortion of the hex elements, we use the energy proposed in [GPW*17], which we summarize here to make the paper self‐contained. We measure the distortion 풟 h ( V ) ( V is a matrix storing the vertex positions of the entire mesh) of each hexahedron h as the sum of the distortions of its decomposition into eight tetrahedra t , one for each corner:…”

Section: Methodsmentioning

confidence: 99%

“…Feature Preservation. The feature is aligned by applying the energy term E B ( V ) proposed in [GPW*17]:…”

Section: Methodsmentioning

confidence: 99%

“…The challenge in our setting is that the mesh we wish to optimize is composed of hexahedra instead of tetrahedra. We propose a novel formulation combining the stitching idea [FL16] with the distortion energy introduced in [GPW*17]. The resulting energy can be efficiently minimized using the solver proposed in [RPPSH17], to obtain a general and effective mechanism to pad hex meshes.…”

Section: Methodsmentioning

confidence: 99%

“…A large family of methods exist to simplify quad [DSSC08, DSC09a, DSC09b, TPC*10, BPP*10] and hexahedral meshes, using sheets collapse operations [BBS02, LS10] or altering the hexahedral duals [TK03, KLSO12]. The topological complexity can also be reduced using local operations [BLK11, TPP*11, MPKZ10, GDC15, GPW*17]. The geometrical quality of a hex‐mesh can also be improved relocating its nodes without changing their connectivity [Knu00, Knu03, BDK*03, WSRRR*12, RGRS14, RGRS*15, LSVT15, XGC18].…”

Section: Related Workmentioning

confidence: 99%

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Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Computer Graphics Forum

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We propose an octree‐based algorithm to tessellate the interior of a closed surface with hexahedral cells. The generated hexahedral mesh (1) explicitly preserves sharp features of the original input, (2) has a maximal, user‐controlled distance deviation from the input surface, (3) is composed of elements with only positive scaled jacobians (measured by the eight corners of a hex [SEK*07]), and (4) does not have self‐intersections. We attempt to achieve these goals by proposing a novel pipeline to create an initial pure hexahedral mesh from an octree structure, taking advantage of recent developments in the generation of locally injective 3D parametrizations to warp the octree boundary to conform to the input surface. Sharp features in the input are bijectively mapped to poly‐lines in the output and preserved by the deformation, which takes advantage of a scaffold mesh to prevent local and global intersections. The robustness of our technique is experimentally validated by batch processing a large collection of organic and CAD models, without any manual cleanup or parameter tuning. All results including mesh data and statistics in the paper are provided in the additional material. The open‐source implementation will be made available online to foster further research in this direction.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

“…Feature Preservation. The feature is aligned by applying the energy term E B ( V ) proposed in [GPW*17]:…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

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Feature Preserving Octree‐Based Hexahedral Meshing

Gao

Shen

Panozzo

2019

Computer Graphics Forum

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Inversion-free geometric mapping construction: A survey

Zhao

et al. 2021

Comp. Visual Media

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A geometric mapping establishes a correspondence between two domains. Since no real object has zero or negative volume, such a mapping is required to be inversion-free. Computing inversion-free mappings is a fundamental task in numerous computer graphics and geometric processing applications, such as deformation, texture mapping, mesh generation, and others. This task is usually formulated as a non-convex, nonlinear, constrained optimization problem. Various methods have been developed to solve this optimization problem. As well as being inversion-free, different applications have various further requirements. We expand the discussion in two directions to (i) problems imposing specific constraints and (ii) combinatorial problems. This report provides a systematic overview of inversion-free mapping construction, a detailed discussion of the construction methods, including their strengths and weaknesses, and a description of open problems in this research field.

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HexaLab.net: An online viewer for hexahedral meshes

Bracci

Tarini

Pietroni

et al. 2019

Computer-Aided Design

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We introduce HexaLab: a WebGL application for real time visualization, exploration and assessment of hexahedral meshes. HexaLab can be used by simply opening www.hexalab.net. Our visualization tool targets both users and scholars. Practitioners who employ hexmeshes for Finite Element Analysis, can readily check mesh quality and assess its usability for simulation. Researchers involved in mesh generation may use HexaLab to perform a detailed analysis of the mesh structure, isolating weak points and testing new solutions to improve on the state of the art and generate high quality images. To this end, we support a wide variety of visualization and volume inspection tools. Our system offers also immediate access to a repository containing all the publicly available meshes produced with the most recent techniques for hexmesh generation. We believe HexaLab, providing a common tool for visualizing, assessing and distributing results, will push forward the recent strive for replicability in our scientific community. Figure 1: A screen-shot of HexaLab running inside Chrome under macOS. Model courtesy of [1]. Intended usagesVisualization: the main function of HexaLab is to serve as an advanced 3D visualizer for hex-meshes, for the purpose of providing a visual insight on the inspected models, and thus, indirectly, on the algorithms that produced them. The visualization of a hex-mesh is complicated by the resolution of the model and, even more so, by the presence of non-trivial 3D internal structures. HexaLab faces this task by offering a set of interactively controlled tools (cutting planes, etc), a shape-revealing realistic lighting (drastically improving the readability of images), novel modalities specifically designed to better communicate the shape of the cells, as well as colormaps and spatial glyphs, to reveal the quality, the topological characteristics, and so on. Assessment: for the same purpose, HexaLab can be used

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Robust structure simplification for hex re-meshing

Cited by 37 publications

References 44 publications

Feature Preserving Octree‐Based Hexahedral Meshing

Feature Preserving Octree‐Based Hexahedral Meshing

Inversion-free geometric mapping construction: A survey

HexaLab.net: An online viewer for hexahedral meshes

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