research-article

Particle-based anisotropic surface meshing

Authors:

Weihua MaoAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 32, Issue 4

Article No.: 99, Pages 1 - 14

https://doi.org/10.1145/2461912.2461946

Published: 21 July 2013 Publication History

Abstract

This paper introduces a particle-based approach for anisotropic surface meshing. Given an input polygonal mesh endowed with a Riemannian metric and a specified number of vertices, the method generates a metric-adapted mesh. The main idea consists of mapping the anisotropic space into a higher dimensional isotropic one, called "embedding space". The vertices of the mesh are generated by uniformly sampling the surface in this higher dimensional embedding space, and the sampling is further regularized by optimizing an energy function with a quasi-Newton algorithm. All the computations can be re-expressed in terms of the dot product in the embedding space, and the Jacobian matrices of the mappings that connect different spaces. This transform makes it unnecessary to explicitly represent the coordinates in the embedding space, and also provides all necessary expressions of energy and forces for efficient computations. Through energy optimization, it naturally leads to the desired anisotropic particle distributions in the original space. The triangles are then generated by computing the Restricted Anisotropic Voronoi Diagram and its dual Delaunay triangulation. We compare our results qualitatively and quantitatively with the state-of-the-art in anisotropic surface meshing on several examples, using the standard measurement criteria.

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Cited By

He JZhang TKobayashi HKawamoto AZhou YNomura TZhu B(2024)Multi-level Partition of Unity on Differentiable Moving ParticlesACM Transactions on Graphics10.1145/368798943:6(1-21)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687989
Xu RLiu LWang NChen SXin SGuo XZhong ZKomura TWang WTu C(2024)CWF: Consolidating Weak Features in High-quality Mesh SimplificationACM Transactions on Graphics10.1145/365815943:4(1-14)Online publication date: 19-Jul-2024
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Genest BCourty NCoeurjolly D(2024)Non‐Euclidean Sliced Optimal Transport SamplingComputer Graphics Forum10.1111/cgf.1502043:2Online publication date: 30-Apr-2024
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Index Terms

Particle-based anisotropic surface meshing
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 32, Issue 4

July 2013

1215 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/2461912

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Copyright © 2013 ACM.

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Publication History

Published: 21 July 2013

Published in TOG Volume 32, Issue 4

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Cited By

He JZhang TKobayashi HKawamoto AZhou YNomura TZhu B(2024)Multi-level Partition of Unity on Differentiable Moving ParticlesACM Transactions on Graphics10.1145/368798943:6(1-21)Online publication date: 19-Dec-2024
https://dl.acm.org/doi/10.1145/3687989
Xu RLiu LWang NChen SXin SGuo XZhong ZKomura TWang WTu C(2024)CWF: Consolidating Weak Features in High-quality Mesh SimplificationACM Transactions on Graphics10.1145/365815943:4(1-14)Online publication date: 19-Jul-2024
https://dl.acm.org/doi/10.1145/3658159
Genest BCourty NCoeurjolly D(2024)Non‐Euclidean Sliced Optimal Transport SamplingComputer Graphics Forum10.1111/cgf.1502043:2Online publication date: 30-Apr-2024
https://doi.org/10.1111/cgf.15020
Lv CLin WZheng J(2024)Adaptively Isotropic Remeshing Based on Curvature Smoothed FieldIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2022.322797030:7(3196-3209)Online publication date: Jul-2024
https://doi.org/10.1109/TVCG.2022.3227970
Zhang JGuo XFeng XZhu LSu X(2024)A complex geometry isosurface reconstruction algorithm for particle based CFD simulationsComputer Physics Communications10.1016/j.cpc.2024.109333305(109333)Online publication date: Dec-2024
https://doi.org/10.1016/j.cpc.2024.109333
Dai YSu JFu X(2024)Anisotropic triangular meshing using metric-adapted embeddingsComputer Aided Geometric Design10.1016/j.cagd.2024.102314111(102314)Online publication date: Jun-2024
https://doi.org/10.1016/j.cagd.2024.102314
Hu AXu KPedrycz WXing M(2024)LiDAR point cloud simplification algorithm with fuzzy encoding-decoding mechanismApplied Soft Computing10.1016/j.asoc.2024.111852162(111852)Online publication date: Sep-2024
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Kim SDoh JHan J(2022)Modeling and rendering non-euclidean spaces approximated with concatenated polytopesACM Transactions on Graphics10.1145/3528223.353018641:4(1-13)Online publication date: 22-Jul-2022
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Zhang WWang QGuo JChai SLiu LFu X(2022)Constrained Remeshing Using Evolutionary Vertex OptimizationComputer Graphics Forum10.1111/cgf.1447141:2(237-247)Online publication date: 24-May-2022
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Khan DPlopski AFujimoto YKanbara MJabeen GZhang YZhang XKato H(2022)Surface Remeshing: A Systematic Literature Review of Methods and Research DirectionsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.301664528:3(1680-1713)Online publication date: 1-Mar-2022
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