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Triangular Bézier Approximations to Constant Mean Curvature Surfaces

  • A. Arnal
  • A. Lluch
  • J. Monterde
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5102)

Abstract

We give a method to generate polynomial approximations to constant mean curvature surfaces with prescribed boundary. We address this problem by finding triangular Bézier extremals of the CMC-functional among all polynomial surfaces with a prescribed boundary. Moreover, we analyze the \(\mathcal{C}^1\) problem, we give a procedure to obtain solutions once the tangent planes for the boundary curves are also given.

Keywords

Control Point Curvature Surface Boundary Curve Polynomial Approximation Tangent Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Arnal, A., Lluch, A., Monterde, J.: Triangular Bézier Surfaces of Minimal Area. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds.) ICCSA 2003. LNCS, vol. 2669, pp. 366–375. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Struwe, M.: Plateau’s problem and the calculus of variations. Mathematical Notes. Princeton University Press, Princeton (1988)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • A. Arnal
    • 1
  • A. Lluch
    • 1
  • J. Monterde
    • 2
  1. 1.Dep. de MatemàtiquesUniversitat Jaume ICastellóSpain
  2. 2.Dep. de Geometria i TopologiaUniversitat de ValènciaBurjassot (València)Spain

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