An n-dimensional Clough-Tocher interpolant

A. J. Worsey, G. Farin

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


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 each n-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.

Original languageEnglish (US)
Pages (from-to)99-110
Number of pages12
JournalConstructive Approximation
Issue number1
StatePublished - Dec 1 1987


  • AMS classification: 41A63, 41A05, 65D05
  • Bernstein-Bézier methods
  • Clough-Tocher elements
  • Multivariate interpolation

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)
  • Computational Mathematics


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