A bivariate \(C^ 2\) Clough-Tocher scheme. (English) Zbl 0597.65005

Alfeld, Peter

Comput. Aided Geom. Des. 1, 257-267 (1984).

Let \({\mathcal D}\) be a two-dimensional domain that has been triangulated. Using the technique of his earlier paper [ibid. 1, 169-181 (1984; Zbl 0566.65003)] the author constructs a bivariate \({\mathcal C}^ 2\)-interpolant on \({\mathcal D}\) that requires \({\mathcal C}^ 2\) data at the scattered points. The scheme is local and has cubic precision.

Reviewer: V.V.Vasil’ev

MSC:

65D05	Numerical interpolation
41A05	Interpolation in approximation theory
41A63	Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)

Keywords:

Clough-Tocher; bivariate interpolation; triangulation; piecewise polynomials

Software:

REDUCE

References:

[1]	Alfeld, P., A trivariate clough-tocher scheme for tetrahedral data, Computer aided geometric design, 1, 169-181, (1984) · Zbl 0566.65003
[2]	Alfeld, P., Multivariate scattered data derivative generation by functional minimization, (1984), submitted for publication
[3]	Alfeld, P., A bivariate C2 clough-tocher scheme, (), January 1984 · Zbl 0597.65005
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