• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文期刊>Geometry, Imaging and Computing >Euclidean formulation of discrete uniformization of the disk
【24h】

Euclidean formulation of discrete uniformization of the disk

机译：欧几里德配制磁盘的离散均匀化

获取原文
获取原文并翻译 | 示例
           
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

Thurston's circle packing approximation of the Riemann Mapping (proven to give the Riemann Mapping in the limit by Rodin- Sullivan) is largely based on the theorem that any topological disk with a circle packing metric can be deformed into a circle packing metric in the disk with boundary circles internally tangent to the circle. The main proofs of the uniformization use hyperbolic volumes (Andreev) or hyperbolic circle packings (by Beardon and Stephenson). We reformulate these problems into a Euclidean context, which allows more general discrete conformal structures and boundary conditions. The main idea is to replace the disk with a double covered disk with one side forced to be a circle and the other forced to have interior curvature zero. The entire problem is reduced to finding a zero curvature structure. We also show that these curvatures arise naturally as curvature measures on generalized manifolds (manifolds with multiplicity) that extend the usual discrete Lipschitz-Killing curvatures on surfaces.
机译：Thurston的圈子包装逼近的riemann映射（已被证明在Rodin-sullivan限制中的Riemann映射）主要是基于定理，其中任何带有圆包装度量的拓扑磁盘可以使磁盘中的圆包装度量变形为边界圈在内部切相向圆圈。均匀化的主要样张使用双曲线（Andrerev）或双曲线圈包装（Beardon和Stephenson）。我们将这些问题重构为欧几里德语境，这允许更通用的离散保形结构和边界条件。主要思想是用双覆盖盘更换磁盘，一侧被迫成为一个圆形，另一侧被迫具有内部曲率零。整个问题减少以找到零曲率结构。我们还表明，这些曲率自然地出现在广义歧管（具有多重性的歧管）上的曲率措施，这些曲线措施在表面上延伸了通常的离散嘴唇杀伤曲率的曲率。

著录项

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号