Discrete Curvature Flows for Surfaces and 3-Manifolds

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 3manifolds 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. Key words: curvature flow, the Ricci flow, Yamabe flow, discrete, surface, 3-manifold

• Type: Conference
• Year: 2008
• Where: ETVC
• Authors: Xiaotian Yin, Miao Jin, Feng Luo 0002, Xianfeng David Gu
• Keywords: Applied Computing, Curvature Flow, Discrete Curvature Flow, ETVC 2008, Yamabe Flow