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Discrete Curvature Flows for Surfaces and 3-Manifolds

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Emerging Trends in Visual Computing (ETVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5416))

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Abstract

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.

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Author information

Authors and Affiliations

  1. Computer Science Department, State University of New York at Stony Brook, USA

    Xiaotian Yin & Xianfeng David Gu

  2. Center for Advanced Computer Studies, University of Louisiana at Lafayette, USA

    Miao Jin

  3. Department of Mathematics, Rutgers University, USA

    Feng Luo

Authors
  1. Xiaotian Yin
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  2. Miao Jin
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  3. Feng Luo
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  4. Xianfeng David Gu
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Editor information

Editors and Affiliations

  1. LIX, Ecole Polytechnique, Route de Saclay, 91128, Palaiseau Cedex, France

    Frank Nielsen

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Yin, X., Jin, M., Luo, F., Gu, X.D. (2009). Discrete Curvature Flows for Surfaces and 3-Manifolds. In: Nielsen, F. (eds) Emerging Trends in Visual Computing. ETVC 2008. Lecture Notes in Computer Science, vol 5416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00826-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-00826-9_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00825-2

  • Online ISBN: 978-3-642-00826-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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