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Interleaving Delaunay refinement and optimization for practical isotropic tetrahedron mesh generation

Jane Tournois, Camille Wormser, Pierre Alliez, Mathieu Desbrun
2009 ACM SIGGRAPH 2009 papers on - SIGGRAPH '09  
Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria.  ...  This interleaving is shown to be more conservative in number of Steiner point insertions than refinement alone, and to produce higher quality meshes than optimization alone.  ...  The authors thank Mariette Yvinec for her constant support, Tamal Dey for his help with DelPSC, and Patrick Mullen for advice.  ... 
doi:10.1145/1576246.1531381 fatcat:6w26rvcmsfdolb3vg6rtlfqedy

Interleaving Delaunay refinement and optimization for practical isotropic tetrahedron mesh generation

Jane Tournois, Camille Wormser, Pierre Alliez, Mathieu Desbrun
2009 ACM Transactions on Graphics  
Building upon recent theoretical and practical advances, our algorithm interleaves Delaunay refinement and mesh optimization to generate quality meshes that satisfy a set of user-defined criteria.  ...  This interleaving is shown to be more sparing in Steiner points' insertions than refinement alone, and to produce higher quality meshes than optimization alone.  ...  Our mesh generation algorithm produces high quality meshes through Delaunay refinements interleaved with Optimal Delaunay optimization.  ... 
doi:10.1145/1531326.1531381 fatcat:gdqto3uqcrheniuomibywixjnm

Unstructured Mesh Generation [chapter]

Jonathan Shewchuk
2012 Combinatorial Scientific Computing  
A seminal triangular meshing paper by Jim Ruppert [94] brought guaranteed good grading and size optimality to Delaunay refinement algorithms.  ...  A Generic Delaunay Refinement Algorithm The early Delaunay mesh generators, like the early advancing front methods, created vertices and triangulated them in two separate stages [47, 23, 59] ; and as  ...  The same questions loom for quadrilateral and hexahedral meshes.  ... 
doi:10.1201/b11644-11 fatcat:zjfel6436jhwlidqrtkvjt3ezy

Adaptive physics based tetrahedral mesh generation using level sets

J. Teran, Neil Molino, R. Fedkiw, R. Bridson
2005 Engineering with Computers  
The resulting mesh is well suited for simulation since it is highly structured, has topology chosen specifically for large deformations, and is readily refined if required during subsequent simulation.  ...  We present a tetrahedral mesh generation algorithm designed for the Lagrangian simulation of deformable bodies.  ...  M. and R. B. were supported in part by a Stanford Graduate Fellowships, and J. T. was supported in part by an NSF Graduate Research Fellowship.  ... 
doi:10.1007/s00366-005-0308-8 fatcat:e7rvipx2w5cxrl3vs23j6q7e74

LpCentroidal Voronoi Tessellation and its applications

Bruno Lévy, Yang Liu
2010 ACM Transactions on Graphics  
The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field).  ...  This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy).  ...  We perform interleaved refinement / optimization of FL p iterations, as done in [Tournois et al. 2009 ] : (1) distribute vertices randomly (2) optimize FL 8 (3) for each refinement iteration (4) insert  ... 
doi:10.1145/1778765.1778856 fatcat:ybaciyttbrgntjgp3ehp7fssty

LpCentroidal Voronoi Tessellation and its applications

Bruno Lévy, Yang Liu
2010 ACM SIGGRAPH 2010 papers on - SIGGRAPH '10  
The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field).  ...  This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy).  ...  We perform interleaved refinement / optimization of FL p iterations, as done in [Tournois et al. 2009 ] : (1) distribute vertices randomly (2) optimize FL 8 (3) for each refinement iteration (4) insert  ... 
doi:10.1145/1833349.1778856 fatcat:kaegquz4o5ctra7aojpszprrci

LpCentroidal Voronoi Tessellation and its applications

Bruno Lévy, Yang Liu
2010 ACM Transactions on Graphics  
The derivations are given for both surface meshing (Ω is a triangulated mesh with per-facet anisotropy) and volume meshing (Ω is the interior of a closed triangulated mesh with a 3D anisotropy field).  ...  This generalization allows for aligning the axes of the Voronoi cells with a predefined background tensor field (anisotropy).  ...  We perform interleaved refinement / optimization of FL p iterations, as done in [Tournois et al. 2009 ] : (1) distribute vertices randomly (2) optimize FL 8 (3) for each refinement iteration (4) insert  ... 
doi:10.1145/1833351.1778856 fatcat:lw6b5ymubvdvfgkbch2aun3do4

Tetrahedral meshing via maximal Poisson-disk sampling

Jianwei Guo, Dong-Ming Yan, Li Chen, Xiaopeng Zhang, Oliver Deussen, Peter Wonka
2016 Computer Aided Geometric Design  
We also propose an efficient optimization strategy to protect the domain boundaries and to remove slivers to improve the meshing quality.  ...  We first perform MPS on the boundary of the input domain, we then sample the interior of the domain, and we finally extract the tetrahedral mesh from the samples by using 3D Delaunay or regular triangulation  ...  ), and Foreign 1000 Talent Plan (WQ201344000169).  ... 
doi:10.1016/j.cagd.2016.02.004 fatcat:45gop6probfnxj4jim2t7a2z2u

Feature-sensitive tetrahedral mesh generation with guaranteed quality

Jun Wang, Zeyun Yu
2012 Computer-Aided Design  
This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model.  ...  A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices.  ...  Acknowledgments The work described was supported in part by an NIH Award (Number R15HL103497) from the National Heart, Lung, and Blood Institute (NHLBI) and by a subcontract from the National Biomedical  ... 
doi:10.1016/j.cad.2012.01.002 pmid:22328787 pmcid:PMC3275789 fatcat:zyetiray5zafbciohx26a4kfza

Revisiting Optimal Delaunay Triangulation for 3D Graded Mesh Generation

Zhonggui Chen, Wenping Wang, Bruno Lévy, Ligang Liu, Feng Sun
2014 SIAM Journal on Scientific Computing  
In this paper, we study the optimal Delaunay triangulation (ODT) for three-dimensional (3D) graded mesh generation. ODT is defined as the minimizer of an objective function [2] .  ...  to generate graded meshes, that satisfies more properties than previous work [32]: it is continuous and Delaunay consistent (section 3); • linear quadratures for estimating the gradient of the ODT energy  ...  The interleaved method operates by alternating Delaunay refinement and ODT optimization. Sliver perturbation is applied as a postprocessing with an angle bound of 20 degrees.  ... 
doi:10.1137/120875132 fatcat:yav6t7xsnfeh3p2edojsmhsdhm

Adaptive and Feature-Preserving Subdivision for High-Quality Tetrahedral Meshes

D. Burkhart, B. Hamann, G. Umlauf
2010 Computer graphics forum (Print)  
We propose a new topology-based refinement operator that generates only tetrahedra and supports adaptive refinement.  ...  We present an adaptive subdivision scheme for unstructured tetrahedral meshes inspired by the √ 3-subdivision scheme for triangular meshes.  ...  Thanks to Klaus Denker for helping us with Figures 1, 8, 9 , and 10.  ... 
doi:10.1111/j.1467-8659.2009.01581.x fatcat:2hniobas7zb3xjbpcluvuexmni

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
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  ...  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  ...  Desbrun, Interleaving delaunay refinement and optimization for practical isotropic tetrahedron mesh generation, ACM Transactions on Graphics 28 (3) (2009) 1. doi:10.1145/1531326.1531381. [58]  ... 
arXiv:1903.09332v2 fatcat:ikoc2la6jrcufmo773zjl4jhpu

Integer-grid maps for reliable quad meshing

David Bommes, Marcel Campen, Hans-Christian Ebke, Pierre Alliez, Leif Kobbelt
2013 ACM Transactions on Graphics  
often cannot be used directly to generate a quadrilateral mesh.  ...  the latter improves the continuous relaxation, which is crucial for the success of modern MIQP optimizers.  ...  Additionally we would like to thank Jan Möbius for the geometry processing framework http://www.OpenFlipper. org and the reviewers for their competent and helpful comments.  ... 
doi:10.1145/2461912.2462014 fatcat:ze32wiezangojmbcoicdrdmyoq

VoroCrust: Voronoi Meshing Without Clipping [article]

Ahmed Abdelkader, Chandrajit L. Bajaj, Mohamed S. Ebeida, Ahmed H. Mahmoud, Scott A. Mitchell, John D. Owens, Ahmad A. Rushdi
2020 ACM Transactions on Graphics   accepted
The VoroCrust algorithm is the first provably-correct algorithm for conforming polyhedral Voronoi meshing for non-convex and non-manifold domains with guarantees on the quality of both surface and volume  ...  A robust refinement process estimates a suitable sizing field that enables the careful placement of Voronoi seeds across the surface circumventing the need for clipping and avoiding its many drawbacks.  ...  While the generation of tetrahedral meshes based on Delaunay refinement [Cheng et al. 2012] or variational optimization [Alliez et al. 2005 ] is well established, research on polyhedral mesh generation  ... 
doi:10.1145/3337680 pmid:32831464 pmcid:PMC7439975 arXiv:1902.08767v2 fatcat:pzylgiubijfo7hoqbn7xthunja

High-Precision 3D Reconstruction for Small-to-Medium-Sized Objects Utilizing Line-Structured Light Scanning: A Review

Bin Cui, Wei Tao, Hui Zhao
2021 Remote Sensing  
However, current research mainly focuses on making adaptive adjustments to various scenarios and related issues in the application of this technology rather than looking for further improvements and enhancements  ...  Meanwhile, a review of approaches, algorithms, and techniques for high-precision 3D reconstruction utilizing line-structured light scanning, which is analyzed from a deeper perspective of elementary details  ...  This algorithm refines the quadrilateral meshes with point mapping and meshes regularization to obtain a high-quality mesh.  ... 
doi:10.3390/rs13214457 fatcat:6pnpg7rxcnaufcrbey2m335lnq
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