Davydov, Oleg; Zeilfelder, Frank Scattered data fitting by direct extension of local polynomials to bivariate splines. (English) Zbl 1065.41017 Adv. Comput. Math. 21, No. 3-4, 223-271 (2004). In this paper the authors study a new stable and efficient method for scattered data fitting capable of dealing with large and possibly noisy data sets with highly varying local density, with voids, clusters and tracks, leading to high quality artifact - free piecewise polynomial surfaces in triangle Bernstein-Bézier form. By using a uniform four-directional mesh they consider the space of C1 piecewise cubics or certain subspaces of C2 splines of degree six. They design for these spaces new minimal determining sets with special features. Several numerical examples are given. Reviewer: Antonio López-Carmona (Granada) Cited in 4 ReviewsCited in 23 Documents MSC: 41A15 Spline approximation 65D15 Algorithms for approximation of functions Keywords:bivariate splines; Approximation:Bernstein-Bézier techniques Software:na17 PDFBibTeX XMLCite \textit{O. Davydov} and \textit{F. Zeilfelder}, Adv. Comput. Math. 21, No. 3--4, 223--271 (2004; Zbl 1065.41017) Full Text: DOI