Discrete Curvature Flows for Surfaces and 3-Manifolds
نویسندگان
چکیده
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.
منابع مشابه
Discrete Curvature Flow for Surfaces and 3-Manifolds
This chapter introduces the concepts, theories and algorithms of discrete curvature flows for surfaces with arbitrary topologies. Discrete curvature flow for hyperbolic 3-manifolds with geodesic boundaries is also presented. Curvature flow method can be used to design Riemannian metrics by prescribed curvatures, and applied for parameterization in graphics, shape registration in computer vision...
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