Abstract
In the present paper we compute for the first time Beta-function B-splines (BFBS) achieving Hermite interpolation up to third partial derivatives at the vertices of the triangulation. We consider examples of BFBS with uniform and variable order of the Hermite interpolation at the vertices of the triangulation, for possibly non-convex star-1 neighbourhoods of these vertices. We also discuss the conversion of the local functions from Taylor monomial bases to appropriately shifted and scaled Bernstein bases, thereby converting the Hermite interpolatory form of the linear combination of BFBS to a new, Bezier-type, form. This conversion is fully parallelized with respect to the vertices of the triangulation and, for Hermite interpolation of uniform order, the load of the computations for each vertex of the computation is readily balanced.
Research partially supported by the 2010 and 2011 Annual Research Grants of the Priority R&D Group for Mathematical Modelling, Numerical Simulation & Computer Visualization at Narvik University College.
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Bang, B., Dechevsky, L.T., Lakså, A., Zanaty, P. (2012). Blending Functions for Hermite Interpolation by Beta-Function B-Splines on Triangulations. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_44
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DOI: https://doi.org/10.1007/978-3-642-29843-1_44
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