The Convergence of Discrete Uniformizations for Genus Zero Surfaces

2021/10/15 by Luo, Yanwen, Wu, Tianqi, Zhu, Xiaoping · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2110.08208

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 ≥ 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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• Convergence of discrete conformal mappings on surfaces

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