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Completeness Characterization of Type-I Box Splines

Nelly Villamizar Orcid Logo, Angelos Mantzaflaris, Bert Jüttler

Geometric Challenges in Isogeometric Analysis. Springer INdAM Series, Volume: 49, Pages: 279 - 304

Swansea University Author: Nelly Villamizar Orcid Logo

  • Accepted Manuscript under embargo until: 9th August 2023

Abstract

We present a completeness characterization of box splines on three-directionaltriangulations, 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 globalsmoothness, our results allow to identify the...

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Published in: Geometric Challenges in Isogeometric Analysis. Springer INdAM Series
ISBN: 9783030923129 9783030923136
ISSN: 2281-518X 2281-5198
Published: Cham Springer International Publishing 2022
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa56991
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Abstract: We present a completeness characterization of box splines on three-directionaltriangulations, 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 globalsmoothness, 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 translatesof 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.
College: Faculty of Science and Engineering
Start Page: 279
End Page: 304