Local (T)HB-spline projectors via restricted hierarchical spline fitting

Alessandro Giust (1) , Bert Jüttler (2) , Angelos Mantzaflaris (3, 4)

1 JKU - University of Linz - Johannes Kepler Universität Linz
2 Institute of Applied Geometry [Linz]
3 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
4 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes

This paper is devoted to techniques for adaptive spline projection via quasi-interpolation, enabling the efficient approximation of given functions. We employ local least-squares fitting in restricted hierarchical spline spaces to establish novel projection operators for hierarchical splines of degree p. This leads to efficient spline projectors that require O(p d) floating point operations and O(1) evaluations of the given function per degree of freedom, while providing essentially the same accuracy as global approximation. Our spline projectors are based on a unifying framework for quasi-interpolation in hierarchical spline spaces. We present a detailed comparison with the scheme of Speleers and Manni (2016).

Mots clés: hierarchical splines; truncation; quasi-interpolation; spline fitting

Domaines: Analyse numérique [math.NA]; Modélisation et simulation; Calcul formel [cs.SC]

Alessandro Giust, Bert Jüttler, Angelos Mantzaflaris. Local (T)HB-spline projectors via restricted hierarchical spline fitting. Computer Aided Geometric Design, 2020, 80, pp.101865. ⟨10.1016/j.cagd.2020.101865⟩. ⟨hal-02985011⟩