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Quintic Spline Interpolation Over Tetrahedral Partitions

Summary: C1
Quintic Spline Interpolation
Over Tetrahedral Partitions
Gerard Awanou and Ming-Jun Lai
Abstract. We discuss the implementation of a C1
quintic super-
spline method for interpolating scattered data in IR3
based on a mod-
ification of Alfeld's generalization of the Clough-Tocher scheme de-
scribed by Lai and LeM´ehaut´e [4]. The method has been implemented
in MATLAB, and we test for the accuracy of reproduction on a basis
of quintic polynomials. We present numerical evidences that when the
partition is refined, the spline interpolant converges to the function to
be approximated.
§1. Introduction
There are a few trivariate spline spaces available for interpolation over a
tetrahedral partition of a polygonal domain in IR3
. We would like to
mention a direct polynomial interpolation by Zenisek in [9]. This scheme
requires piecewise polynomials of degree 9 and is globally C1


Source: Awanou, Gerard - Department of Mathematical Sciences, Northern Illinois University


Collections: Mathematics