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.
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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)
Struwe, M.: Plateau’s problem and the calculus of variations. Mathematical Notes. Princeton University Press, Princeton (1988)
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Arnal, A., Lluch, A., Monterde, J. (2008). Triangular Bézier Approximations to Constant Mean Curvature Surfaces. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds) Computational Science – ICCS 2008. ICCS 2008. Lecture Notes in Computer Science, vol 5102. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69387-1_11
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DOI: https://doi.org/10.1007/978-3-540-69387-1_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69386-4
Online ISBN: 978-3-540-69387-1
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