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)


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.


Control Point Curvature Surface Boundary Curve Polynomial Approximation Tangent Plane 
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    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
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    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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