A trivariate clough-tocher scheme for tetrahedral data

Authors:
Peter Alfeld
Affiliations:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, U.S.A.
Venue:
Computer Aided Geometric Design
Year:
1984

Citing 0
Cited 9

Two tetrahedral C1 cubic macro elements

Journal of Approximation Theory
A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions

Journal of Approximation Theory
Quasi-interpolation by quadratic piecewise polynomials in three variables

Computer Aided Geometric Design
A C2 trivariate macro-element based on the Clough--Tocher-split of a tetrahedron

Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Dimension of C1-splines on type-6 tetrahedral partitions

Journal of Approximation Theory
A bivariate C2 Clough-Tocher scheme

Computer Aided Geometric Design
An iterative method for computing multivariate C1 piecewise polynomial interpolants

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Surfaces in computer aided geometric design: a survey with new results

Computer Aided Geometric Design
Full length article: A C r trivariate macro-element based on the Alfeld split of tetrahedra

Journal of Approximation Theory

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Abstract

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.