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Recent Advances in Computational Conformal Geometry

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Mathematics of Surfaces XIII (Mathematics of Surfaces 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5654))

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Abstract

Computational conformal geometry focuses on developing the computational methodologies on discrete surfaces to discover conformal geometric invariants. In this work, we briefly summarize the recent developments for methods and related applications in computational conformal geometry. There are two major approaches, holomorphic differentials and curvature flow. The holomorphic differential method is a linear method, which is more efficient and robust to triangulations with lower quality. The curvature flow method is nonlinear and requires higher quality triangulations, but more flexible. The conformal geometric methods have been broadly applied in many engineering fields, such as computer graphics, vision, geometric modeling and medical imaging. The algorithms are robust for surfaces scanned from real life, general for surfaces with different topologies. The efficiency and efficacy of the algorithms are demonstrated by the experimental results.

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Author information

Authors and Affiliations

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

    X. D. Gu

  2. Mathematics Department, Rutgers University, USA

    F. Luo

  3. Mathematics Department, Harvard University, USA

    S. -T. Yau

Authors
  1. X. D. Gu
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  2. F. Luo
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  3. S. -T. Yau
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Editor information

Editors and Affiliations

  1. Computer Vision and Pattern Recognition Group,Computer Science, University of York Heslington, YO10-5DD, York, United Kingdom

    Edwin R. Hancock

  2. School of Computer Science, Cardiff University, Cardiff, UK

    Ralph R. Martin

  3. Numerical Geometry Ltd, 26 Abbey Lane, Lode, CB5 9EP, Cambridge, UK

    Malcolm A. Sabin

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© 2009 Springer-Verlag Berlin Heidelberg

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Gu, X.D., Luo, F., Yau, S.T. (2009). Recent Advances in Computational Conformal Geometry. In: Hancock, E.R., Martin, R.R., Sabin, M.A. (eds) Mathematics of Surfaces XIII. Mathematics of Surfaces 2009. Lecture Notes in Computer Science, vol 5654. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03596-8_11

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  • DOI: https://doi.org/10.1007/978-3-642-03596-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03595-1

  • Online ISBN: 978-3-642-03596-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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