Publications

Papers & preprints

Theory and algorithms for surface and volume parameterization.

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Preprints

A Discrete-to-Continuum Variational Theory for Area-Preserving Surface Parameterization

arXiv:2608.17873, 2026

S.-Y. Liu, Kento Sakai, M.-H. Yueh

Links stretch energy and area preservation across mesh refinement.

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@misc{LiKY26,
  author        = {Shu-Yung Liu and Kento Sakai and Mei-Heng Yueh},
  title         = {A Discrete-to-Continuum Variational Theory for Area-Preserving Surface Parameterization},
  year          = {2026},
  archiveprefix = {arXiv},
  eprint        = {2608.17873},
  primaryclass  = {math.NA},
}

Journal articles

Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method

Journal of Optimization Theory and Applications, 209, Article 68, 2026

S.-Y. Liu, T.-M. Huang, W.-W. Lin, M.-H. Yueh

Maps solids onto a ball while minimizing volume distortion.

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@article{LiHL26,
  author  = {Liu, S.-Y. and Huang, T.-M. and Lin, W.-W. and Yueh, M.-H.},
  title   = {Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method},
  journal = {J. Optim. Theory Appl.},
  volume  = {209},
  number  = {3},
  pages   = {68},
  year    = {2026},
  issn    = {1573-2878},
  doi     = {10.1007/s10957-026-03002-5},
}

Spherical Area-Preserving Parameterization via Energy Minimization

SIAM Journal on Imaging Sciences, 19(1):207–235, 2026

S.-Y. Liu, M.-H. Yueh

Computes spherical area-preserving maps with bijective correction.

Full text arXiv Highlight GitHub

@article{LiYu26,
  author  = {Liu, S.-Y. and Yueh, M.-H.},
  title   = {Spherical Area-Preserving Parameterization via Energy Minimization},
  journal = {SIAM J. Imaging Sci.},
  volume  = {19},
  number  = {1},
  pages   = {207--235},
  year    = {2026},
  doi     = {10.1137/25M1736979},
}

Energy-Based Distortion-Balancing Parameterization for Open Surfaces

SIAM Journal on Imaging Sciences, 18(4):2059–2093, 2025

S.-Y. Liu, M.-H. Yueh

Flattens surfaces while balancing angle and area distortion.

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@article{LiYu25,
  author  = {Liu, S.-Y. and Yueh, M.-H.},
  title   = {Energy-Based Distortion-Balancing Parameterization for Open Surfaces},
  journal = {SIAM J. Imaging Sci.},
  volume  = {18},
  number  = {4},
  pages   = {2059--2093},
  year    = {2025},
  doi     = {10.1137/24M1708437},
}

Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations

Journal of Scientific Computing, 100(2):43, 2024

S.-Y. Liu, M.-H. Yueh

Minimizes disk area distortion with a globally convergent solver.

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@article{LiYu24,
  author  = {Liu, S.-Y. and Yueh, M.-H.},
  title   = {Convergent Authalic Energy Minimization for Disk Area-Preserving Parameterizations},
  journal = {J. Sci. Comput.},
  volume  = {100},
  number  = {2},
  pages   = {43},
  year    = {2024},
  issn    = {1573-7691},
  doi     = {10.1007/s10915-024-02594-2},
}