Spherical Area-Preserving Parameterization via Energy Minimization

Shu-Yung Liu; Mei-Heng Yueh

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arXiv · 2412.19011

Spherical Area-Preserving Parameterization via Energy Minimization

Shu-Yung Liu·Mei-Heng Yueh

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Abstract

We propose a novel method, called spherical authalic energy minimization (SAEM), for computing spherical area-preserving parameterizations of genus-zero closed surfaces, with strong theoretical foundations. The global convergence of the associated computational algorithm is theoretically guaranteed. In addition, we introduce a Riemannian bijective correction method that ensures the bijectivity of the resulting mapping under mild assumptions. Numerical experiments show that SAEM effectively minimizes area distortion and achieves bijective mappings, outperforming state-of-the-art methods. Finally, we demonstrate the practical utility of SAEM in shape description.

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Shu-Yung Liu, Mei-Heng Yueh. 2024-12-26. Spherical Area-Preserving Parameterization via Energy Minimization. https://arxiv.org/abs/2412.19011

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