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Compute Quasi-Conformal Map on Point Cloud by Point Integral Method

Zhen Li Tsinghua University Zuoqiang Shi Tsinghua University Jian Sun Tsinghua University

Numerical Analysis and Scientific Computing mathscidoc:1711.25002

We develop a method searching for quasi-conformal maps from point-cloud surfaces to Euclidean plane. The maps can be got by directly solving Beltrami equation with proper boundary condition or solving optimization problem of the variational formu- lation. The point integral methd (PIM) is used for discretization on point clouds. Numerical experiments suggest that the method converges as the density of points in- creases.
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@inproceedings{zhencompute,
  title={Compute Quasi-Conformal Map on Point Cloud by Point Integral Method},
  author={Zhen Li, Zuoqiang Shi, and Jian Sun},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171107105813531185853},
}
Zhen Li, Zuoqiang Shi, and Jian Sun. Compute Quasi-Conformal Map on Point Cloud by Point Integral Method. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20171107105813531185853.
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