Completeness characterization of Type-I box splines - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year :

Completeness characterization of Type-I box splines

(1) , (2, 3) , (4)
1
2
3
4

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.
Fichier principal
Vignette du fichier
paper_indam.pdf (645.18 Ko) Télécharger le fichier
Vignette du fichier
vignette.png (88.58 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image
Loading...

Dates and versions

hal-02991234 , version 1 (05-11-2020)

Identifiers

  • HAL Id : hal-02991234 , version 1

Cite

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

Share

Gmail Facebook Twitter LinkedIn More