Three- and four-dimensional surfaces. (English) Zbl 0552.65008

Barnhill, R. E.; Little, F. F.

Rocky Mt. J. Math. 14, 77-102 (1984).

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

MSC:

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)

Keywords:

triangular patches: tetrahedral patches; local interpolation methods; multivariate scattered data; Barnhill-Birkhoff-Gordon scheme; radial Nielson scheme; gradient estimation