Mallock and Clough: A Correction

Cubic precision Clough-Tocher interpolation

The standard Clough-Tocher split-domain scheme constructs a surface element with quadratic precision. In this paper, I will look at methods for improving the degrees of freedom in Clough-Tocher schemes. In particular , I will discuss modiications to the cross-boundary construction that improve the interpolant from quadratic precision to cubic precision. In the general scattered data interpolati...

A C1 Multivariate Clough–Tocher Interpolant

We show that in dimensions four and higher, to insure a smooth interpolant, additional geometric constraints must be imposed on the generalized Clough–Tocher split introduced in Worsey and Farin (Constr. Approx. 3:99–110, 1987).

Polynomial Pre ision Clough-To her Interpolation

Simplex–Splines on the Clough–Tocher Element

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A trivariate clough-tocher scheme for tetrahedral data

An interpolation scheme is described for values of position, gradient and Hessian at scattered points in three variables. The domain is assumed to have been tesselated into tetrahedra. The interpolant has local support, is globally once differentiable, piecewise polynomial, and reproduces polynomials of degree up to three exactly. The scheme has been implemented in a FORTRAN research code. AMS ...