A Convergent Conformal Energy Minimization for the Computation of Disk Parameterizations

Yueh-Cheng Kuo National University of Kaohsiung Wen-Wei Lin National Yang Ming Chiao Tung University Mei-Heng Yueh National Taiwan Normal University Shing-Tung Yau Harvard University

Computational Geometry mathscidoc:2104.09001

Surface conformal parameterizations have been widely applied to various tasks in computer graphics. In this paper, we develop a convergent conformal energy minimization (CCEM) iterative algorithm via the line-search gradient descent method with a quadratic approximation for the computation of disk-shaped conformal parameterizations of simply connected open triangular meshes. In addition, we prove the global convergence of the proposed CCEM iterative algorithm. Moreover, under some mild assumptions, we prove the existence of the nontrivial solution, which is a local minimum of the conformal energy with a bijective boundary map. Numerical experiments indicate that the efficiency of the proposed CCEM algorithm is highly improved and the accuracy is competitive with that of state-of-the-art algorithms.
disk conformal parameterization, conformal energy minimization, simply connected open surface
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@inproceedings{yueh-chenga,
  title={A Convergent Conformal Energy Minimization for the Computation of Disk Parameterizations},
  author={Yueh-Cheng Kuo, Wen-Wei Lin, Mei-Heng Yueh, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210426233923968090797},
}
Yueh-Cheng Kuo, Wen-Wei Lin, Mei-Heng Yueh, and Shing-Tung Yau. A Convergent Conformal Energy Minimization for the Computation of Disk Parameterizations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20210426233923968090797.
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