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Three- and four-dimensional surfaces. (English) Zbl 0552.65008
This paper discusses a variety of local interpolation methods to multivariate scattered data. The interpolants are functions from \({\mathbb{R}}^ 2\to {\mathbb{R}}^ 1\) and \({\mathbb{R}}^ 3\to {\mathbb{R}}^ 1\), and they are defined over a collection of triangles or tetrahedra, respectively. The surface schemes that are discussed are a) Barnhill- Birkhoff-Gordon scheme, and b) a radial Nielson scheme. These surface schemes are also discretized. Apart from this, a detailed treatment is given to the partition of the domain into triangles, respectively tetrahedra as well as to the preprocessing step of gradient estimation.
Reviewer: G.Farin

65D05 Numerical interpolation
53A05 Surfaces in Euclidean and related spaces
41A05 Interpolation in approximation theory
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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