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<TITLE>Riemann Surface :Publications :Abstract : Discrete Curvature Flow for Hyperbolic 3-Manifolds with Complete Geodesic Boundaries</TITLE>
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<H3> Discrete Curvature Flow for Hyperbolic 3-Manifolds with Complete Geodesic Boundaries</H3>
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poster in 6th Eurographics Symposium on Geometry Processing (SGP) 2008
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Xiaotian Yin, Miao Jin, Feng Luo and Xianfeng Gu
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Every surface in the three dimensional Euclidean space have a canonical Riemannian
metric, which induces constant Gaussian curvature and is conformal to the original 
metric. Discrete curvature flow is a feasible way to compute such canonical metrics. 
Similarly, three dimensional manifolds also admit canonical metrics, which induce 
constant sectional curvature. Canonical metrics on 3-manifolds are valuable for the 
study of 3D topology and have the potential for volumetric parameterization and shape matching.
This paper generalizes discrete curvature flow from surfaces to hyperbolic 3-manifolds 
with complete geodesic boundaries. The metric deforms according to the curvature, until 
the curvature is constant everywhere. The theoretical results are introduced, the 
algorithm is explained in details, and thorough experiments are carried out to 
demonstrate the effectiveness and efficiency of discrete 3-manifold
curvature flow.
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