An Efficient Energy Minimization for Conformal Parameterizations

Mei Heng Yueh*, Wen-Wei Lin, Chin-Tien Wu, Shing Tung Yau

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


Surface parameterizations have been widely applied to digital geometry processing. In this paper, we propose an efficient conformal energy minimization (CEM) algorithm for computing conformal parameterizations of simply-connected open surfaces with a very small angular distortion and a highly improved computational efficiency. In addition, we generalize the proposed CEM algorithm to computing conformal parameterizations of multiply-connected surfaces. Furthermore, we prove the existence of a nontrivial accumulation point of the proposed CEM algorithm under some mild conditions. Several numerical results show the efficiency and robustness of the CEM algorithm comparing to the existing state-of-the-art algorithms. An application of the CEM on the surface morphing between simply-connected open surfaces is demonstrated thereafter. Thanks to the CEM algorithm, the whole computations for the surface morphing can be performed efficiently and robustly.

Original languageEnglish
Pages (from-to)203-227
Number of pages25
JournalJournal of Scientific Computing
Issue number1
StatePublished - 1 Oct 2017


  • Conformal energy minimization
  • Conformal parameterizations
  • Simply-connected open surfaces
  • Surface morphing

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