Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations

Shu Yung Liu, Mei Heng Yueh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


An area-preserving parameterization of a surface is a bijective mapping that maps the surface onto a specified domain and preserves the local area. This paper formulates the computation of disk area-preserving parameterization as an improved optimization problem and develops a preconditioned nonlinear conjugate gradient method with guaranteed theoretical convergence for solving the problem. Numerical experiments indicate that our new approach has significantly improved area-preserving accuracy and computational efficiency compared to other state-of-the-art algorithms. Furthermore, we present an application of surface registration to illustrate the practical utility of area-preserving mappings as parameterizations of surfaces.

Original languageEnglish
Article number43
JournalJournal of Scientific Computing
Issue number2
Publication statusPublished - 2024 Aug


  • Area-preserving parameterization
  • Authalic energy minimization
  • Nonlinear conjugate gradient method
  • Simplicial mapping
  • Simplicial surface

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • General Engineering
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


Dive into the research topics of 'Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations'. Together they form a unique fingerprint.

Cite this