Shape-preserving approximation of spatial data
The authors combine the approach of \textit{P. Costantini} and \textit{F. Pelosi} [Numer. Algorithms 27, 237--264 (2001; Zbl 1079.65018)] with the results of \textit{P. Costantini} and \textit{C. Manni} [Adv. Comput. Math. 18, No. 1, 41--63 (2003; Zbl 1018.65017)] and obtain \(C^3\) shape-preserving splines, approximating an ordered set of spatial data. First, the shape of the data is defined and a precise formulation of the shape constraints is provided. Next, the B-splines like basis are computed. These approximating splines satisfy boundary conditions. The precise statement of the best approximation problem and the analysis of asymptotic properties of the splines are also provided. Algorithms for global and semilocal shape-preserving approximation are presented. Finally, some graphical examples are presented.
scientific article; zbMATH DE number 2057581