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Minimal Mean-Curvature-Variation Surfaces and Their Applications in Surface Modeling

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Book cover Geometric Modeling and Processing - GMP 2006 (GMP 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4077))

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Abstract

Physical based and geometric based variational techniques for surface construction have been shown to be advanced methods for designing high quality surfaces in the fields of CAD and CAGD. In this paper, we derive a Euler-Lagrange equation from a geometric invariant curvature integral functional–the integral about the mean curvature gradient. Using this Euler-Lagrange equation, we construct a sixth-order geometric flow (named as minimal mean-curvature-variation flow), which is solved numerically by a divided-difference-like method. We apply our equation to solving several surface modeling problems, including surface blending, N-sided hole filling and point interpolating. The illustrative examples provided show that this sixth-order flow yields high quality surfaces.

Project supported in part by NSFC grant 10371130 and National Key Basic Research Project of China (2004CB318000). The second author is also supported in part by the NSFC grant 10571012 and the Beijing Natural Science Foundation 1062005.

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Author information

Authors and Affiliations

  1. LSEC, Institute of Computational Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China

    Guoliang Xu

  2. Department of Basic Courses, Beijing Information Science and Technology, University, Beijing, 100085, China

    Qin Zhang

Authors
  1. Guoliang Xu
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  2. Qin Zhang
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Editor information

Editors and Affiliations

  1. Seoul National University, Korea

    Myung-Soo Kim

  2. Carnegie Mellon University, Pittsburgh, PA, USA

    Kenji Shimada

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© 2006 Springer-Verlag Berlin Heidelberg

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Xu, G., Zhang, Q. (2006). Minimal Mean-Curvature-Variation Surfaces and Their Applications in Surface Modeling. In: Kim, MS., Shimada, K. (eds) Geometric Modeling and Processing - GMP 2006. GMP 2006. Lecture Notes in Computer Science, vol 4077. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11802914_25

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  • DOI: https://doi.org/10.1007/11802914_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36711-6

  • Online ISBN: 978-3-540-36865-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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