论文标题
封闭表面离散均匀化的收敛性
The Convergence of Discrete Uniformizations for Closed Surfaces
论文作者
论文摘要
三角形网格上离散的相结合的概念具有丰富的数学理论和广泛的应用。三角形网格上离散均匀化的相关概念提出了计算表面均匀化的有效方法。本文证明，当近似三角形网格相当好时，离散的均匀化近似于$ \ geq1 $的闭合表面的连续均匀化。据作者所知，这是计算属属$> 1 $表面均匀化的第一个收敛结果。
The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations of surfaces. This paper proves that the discrete uniformizations approximate the continuous uniformization for closed surfaces of genus $\geq1$, when the approximating triangle meshes are reasonably good. To the best of the authors' knowledge, this is the first convergence result on computing uniformizations for surfaces of genus $>1$.
