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Ann-dimensional Clough-Tocher interpolant

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Abstract

We consider the problem of C1 interpolation to data given at the vertices and mid-edge points of a tessellation in Rn. The given data are positional and gradient information at the vertices, together with the gradient at the mid-edge points. By subdividing eachn-simplex in an appropriate way, we show how to solve the interpolation problem using piecewise cubic polynomials. The subdivision process is the key to the method and is inductive in nature. It is systematically built up from the two-dimensional case where a variant of the well-known Clough-Tocher element is used.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of North Carolina at Wilmington, 28403, Wilmington, North Carolina, USA

    A. J. Worsey

  2. Department of Computer Science, Arizona State University, 58287, Tempe, Arizona, USA

    G. Farin

Authors
  1. A. J. Worsey
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  2. G. Farin
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Communicated by Klaus Höllig.

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Worsey, A.J., Farin, G. Ann-dimensional Clough-Tocher interpolant. Constr. Approx 3, 99–110 (1987). https://doi.org/10.1007/BF01890556

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  • DOI: https://doi.org/10.1007/BF01890556

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