Fast Disk Conformal Parameterization for Simply-connected Open Surfaces

Pui-Tung Choi The Chinese University of Hong Kong Ronald Lok Ming Lui The Chinese University of Hong Kong

Computational Geometry mathscidoc:1609.09008

Computer Vision and Pattern Recognition, 65, (3), 1065-1090, 2015.12
Surface parameterizations have been widely used in computer graphics and geometry processing. In particular, as simply-connected open surfaces are conformally equivalent to the unit disk, it is desirable to compute the disk conformal parameterizations of the surfaces. In this paper, we propose a novel algorithm for the conformal parameterization of a simply-connected open surface onto the unit disk, which signifi cantly speeds up the computation, enhances the conformality and stability, and guarantees the bijectivity. The conformality distortions at the inner region and on the boundary are corrected by two steps, with the aid of an iterative scheme using quasi-conformal theories. Experimental results demonstrate the eff ectiveness of our proposed method.
Disk conformal parameterization, Simply-connected open surface, Beltrami di fferential, Conformal Geometry, Quasi-conformal theory
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@inproceedings{pui-tung2015fast,
  title={Fast Disk Conformal Parameterization for Simply-connected Open Surfaces},
  author={Pui-Tung Choi, and Ronald Lok Ming Lui},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905161119299202620},
  booktitle={Computer Vision and Pattern Recognition},
  volume={65},
  number={3},
  pages={1065-1090},
  year={2015},
}
Pui-Tung Choi, and Ronald Lok Ming Lui. Fast Disk Conformal Parameterization for Simply-connected Open Surfaces. 2015. Vol. 65. In Computer Vision and Pattern Recognition. pp.1065-1090. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160905161119299202620.
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