No Cover Image

Conference Paper/Proceeding/Abstract 515 views

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

Full text not available from this repository: check for access using links below.

Check full text

DOI (Published version): 10.1007/978-3-030-92313-6_12

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...

Full description

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
Tags: Add Tag
No Tags, Be the first to tag this record!
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

Similar Items