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A characterization of certain \(C^ 1\) discrete triangular interpolants. (English) Zbl 0593.65008
Author’s summary: Triangular interpolants have been receiving attention recently as a tool for use in free form surface design in computer aided design environments. Traditionally, rectangular patches have been used in most applications; however there are many surfaces whose shapes do not lend themselves to being split into rectangular patches. Such situations often arise in modeling closed surfaces, or at the join of two rectangular patch arrays as in the wing and body of an airplane. Triangular interpolants can often lead to a natural solution in such cases. In this paper we characterize a certain class of \(C^ 1\) discrete triangular interpolants. The class considered is meant to represent a natural set of interpolants usable in computer aided design environment. Several such interpolants from the literature are pointed out.
Reviewer: E.Morgantini

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