On the local approximation power of quasi-hierarchical powell-sabin splines

Authors:
Hendrik Speleers;Paul Dierckx;Stefan Vandewalle
Affiliations:
Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium;Department of Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium
Venue:
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Year:
2008

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Abstract

Quasi-hierarchical Powell-Sabin (QHPS) splines are quadratic splines with a global C1-continuity. They are defined on a locally refined hierarchical triangulation, and they admit a compact representation in a normalized B-spline basis. We show that sufficiently smooth functions and their derivatives can be approximated up to optimal order by a Hermite interpolating QHPS spline.