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- Title
The Convergence of Discrete Uniformizations for Genus Zero Surfaces.
- Authors
Luo, Yanwen; Wu, Tianqi; Zhu, Xiaoping
- Abstract
The notion of discrete conformality proposed by Luo (2004) and Bobenko et al. (2015) on triangle meshes has rich mathematical theories and wide applications. Gu et al. (2019) and Wu and Zhu (2020) 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.
- Subjects
SPHERICAL projection; CONFORMAL geometry; HYPERBOLIC geometry; TRIANGLES; CONVEX surfaces
- Publication
Discrete & Computational Geometry, 2024, Vol 71, Issue 3, p1057
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-022-00458-w