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Scattered data interpolation and approximation using bivariate \(C^{1}\) piecewise cubic polynomials. (English) Zbl 0873.65011
Summary: We show that if the scattered data over a polygonal domain can be quadrangulated, then the space of bivariate \(C^{1}\) piecewise cubic polynomial functions on a triangulation obtained from the quadrangulation has the full approximation order. We point out that our method is more efficient than the Clough-Tocher scheme.

65D17 Computer-aided design (modeling of curves and surfaces)
68U07 Computer science aspects of computer-aided design
65D07 Numerical computation using splines
Full Text: DOI
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