No Cover Image

Journal article 41 views

Completeness characterization of Type-I Box Splines / Nelly Villamizar, Angelos Mantzaflaris, Bert Juettler

Springer INdAM Series: Geometric Challenges in Isogeometric Analysis

Swansea University Author: Nelly Villamizar

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: Springer INdAM Series: Geometric Challenges in Isogeometric Analysis
Published:
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: College of Science