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Blending Functions for Hermite Interpolation by Beta-Function B-Splines on Triangulations

  • Børre Bang
  • Lubomir T. Dechevsky
  • Arne Lakså
  • Peter Zanaty
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)

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.

Keywords

Lagrange Interpolation Hermite Interpolation Taylor Polynomial Triangular Patch Uniform Order 
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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Børre Bang
    • 1
  • Lubomir T. Dechevsky
    • 1
  • Arne Lakså
    • 1
  • Peter Zanaty
    • 1
  1. 1.Priority R&D Group for Mathematical Modelling, Numerical Simulation & Computer Visualization, Faculty of TechnologyNarvik University CollegeNarvikNorway

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