The paper presents some properties of Generalized T-splines (GT-splines), which are crucial to their actual application. In particular, we construct a dual basis for a noteworthy class of GTsplines, which allows to show that, under suitable conditions, they form a partition of unity. Moreover, we study the approximation properties of the GT-spline space by constructing a class of quasi-interpolants which belong to it and are defined by giving a dual basis.
On the approximation power of generalized T-splines
BRACCO, CESARE;DAGNINO, Catterina;
2017-01-01
Abstract
The paper presents some properties of Generalized T-splines (GT-splines), which are crucial to their actual application. In particular, we construct a dual basis for a noteworthy class of GTsplines, which allows to show that, under suitable conditions, they form a partition of unity. Moreover, we study the approximation properties of the GT-spline space by constructing a class of quasi-interpolants which belong to it and are defined by giving a dual basis.
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