The Convergence of Discrete Uniformizations for Genus Zero Surfaces

Yanwen Luo; Tianqi Wu; Xiaoping Zhu

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arXiv · 2110.08208

The Convergence of Discrete Uniformizations for Genus Zero Surfaces

Yanwen Luo·Tianqi Wu·Xiaoping Zhu

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Abstract

The notion of discrete conformality proposed by Luo and Bobenko-Pinkall-Springborn on triangle meshes has rich mathematical theories and wide applications. Gu et al. proved that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus $\geq 1$, given that the approximating triangle meshes are reasonably good. In this paper, we generalize this result to the remaining case of genus-zero surfaces, by reducing it to planar cases via stereographic projections.

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Yanwen Luo, Tianqi Wu, Xiaoping Zhu. 2021-10-15. The Convergence of Discrete Uniformizations for Genus Zero Surfaces. https://arxiv.org/abs/2110.08208

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