Hooke's Optimization for 3D Triangular Mesh

Hei Long Chan The Chinese University of Hong Kong Ho Yeung Hung The Chinese University of Hong Kong Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09011

Journal of Geometry, Imaging and Computing, 2, (2), 109 – 131, 2015
A fresh framework for mesh optimization, the Filtered Hooke's Optimization, is proposed. With the notion of the elasticity theory, the Hooke's Optimization is developed by modifying the Hooke's law, in which an elastic force is simulated on the edges of a mesh so that adjacent vertices are either attracted to each other or repelled from each other, so as to regularize the mesh in terms of triangulation. A normal torque force is acted on vertices to guarantee smoothness of the surface. In addition, a filtering scheme, called the Newtonian Filtering, is proposed as a supplementary tool for the proposed Hooke's Optimization to preserve the geometry of the mesh. Numerical simulations on meshes with diff erent geometry indicate an impressive performance of our proposed framework to signifi cantly improve the mesh triangulation without noteworthy distortions of the mesh geometry.
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@inproceedings{hei2015hooke's,
  title={Hooke's Optimization for 3D Triangular Mesh},
  author={Hei Long Chan, Ho Yeung Hung, and Ronald Lok Ming Lui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905165401259276623},
  booktitle={Journal of Geometry, Imaging and Computing},
  volume={2},
  number={2},
  pages={109 – 131},
  year={2015},
}
Hei Long Chan, Ho Yeung Hung, and Ronald Lok Ming Lui. Hooke's Optimization for 3D Triangular Mesh. 2015. Vol. 2. In Journal of Geometry, Imaging and Computing. pp.109 – 131. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905165401259276623.
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