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Completeness characterization of Type-I box splines

Nelly Villamizar 1 Angelos Mantzaflaris 2, 3 Bert Jüttler 4
2 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : We present a completeness characterization of box splines on three-directional triangulations, also called Type-I box spline spaces, based on edge-contact smoothness properties. For any given Type-I box spline, of specific maximum degree and order of global smoothness, our results allow to identify the local linear subspace of polynomials spanned by the box spline translates. We use the global super-smoothness properties of box splines as well as the additional super-smoothness conditions at edges to characterize the spline space spanned by the box spline translates. Subsequently, we prove the completeness of this space space with respect to the local polynomial space induced by the box spline translates. The completeness property allows the construction of hierarchical spaces spanned by the translates of box splines for any polynomial degree on multilevel Type-I grids. We provide a basis for these hierarchical box spline spaces under explicit geometric conditions of the domain.
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https://hal.inria.fr/hal-02991234
Contributor : Angelos Mantzaflaris <>
Submitted on : Thursday, November 5, 2020 - 9:48:20 PM
Last modification on : Thursday, November 26, 2020 - 3:50:03 PM

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Nelly Villamizar, Angelos Mantzaflaris, Bert Jüttler. Completeness characterization of Type-I box splines. 2020. ⟨hal-02991234⟩

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