Convergent Conformal Energy Minimization for the Computation of Disk Parameterizations

Yueh Cheng Kuo, Wen Wei Lin, Mei Heng Yueh, Shing Tung Yau

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


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 a nontrivial solution, which is a local minimum of the conformal energy with a bijective boundary map. The numerical experiments indicate that the efficiency of the proposed CCEM algorithm is greatly improved and that the accuracy is competitive with that of state-of-the-art algorithms.

Original languageEnglish
Pages (from-to)1790-1815
Number of pages26
JournalSIAM Journal on Imaging Sciences
Issue number4
Publication statusPublished - 2021


  • conformal energy minimization
  • disk conformal parameterization
  • simply connected open surface

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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