Discrete Curvature Flows for Surfaces and 3-Manifolds
Discrete Curvature Flows for Surfaces and 3-Manifolds
复制标题
DOI：
10.1007/978-3-642-00826-9_3
复制
发表时间：
2009-03
期刊：
影响因子：
--
通讯作者：
Xiaotian Yin;Miao Jin;F. Luo;X. Gu
中科院分区：
文献类型：
--
作者：
Xiaotian Yin;Miao Jin;F. Luo;X. Gu
内禀曲率流可以用来设计黎曼度量。本章介绍了三种最近被引入工程领域的离散曲率流方法：各种拓扑曲面的离散Ricci流和离散Yamabe流，以及带边界的双曲三维流形的离散曲率流。对于每一个流，我们介绍了它的理论，在光滑设置和离散设置，加上数值算法来计算它。我们还提供了一个简短的调查，他们的历史和他们的联系，在计算机图形学，计算机视觉，医学成像，计算机辅助设计和其他一些工程应用。
Intrinsic curvature flows can be used to design Riemannian metrics by prescribed curvatures. This chapter presents three discrete curvature flow methods that are recently introduced into the engineering fields: the discrete Ricci flow and discrete Yamabe flow for surfaces with various topology, and the discrete curvature flow for hyperbolic 3-manifolds with boundaries. For each flow, we introduce its theories in both the smooth setting and the discrete setting, plus the numerical algorithms to compute it. We also provide a brief survey on their history and their link to some of the engineering applications in computer graphics, computer vision, medical imaging, computer aided design and others.