Generalized spline spaces over T-meshes: Dimension formula and locally refined generalized B-splines

Univariate generalized splines are smooth piecewise functions with sections in certain extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) polynomial splines, and enjoy the same structural properties as their polynomial counterparts. In this paper, we consider general...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 272; pp. 187 - 198
Main Authors: Bracco, Cesare, Lyche, Tom, Manni, Carla, Roman, Fabio, Speleers, Hendrik
Format: Journal Article
Language:English
Published: Elsevier Inc 01.01.2016
Subjects:
Dimension formula
Generalized splines
LR-meshes
T-meshes
Generalized splines
T-meshes
LR-meshes
Dimension formula
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:Univariate generalized splines are smooth piecewise functions with sections in certain extended Tchebycheff spaces. They are a natural extension of univariate (algebraic) polynomial splines, and enjoy the same structural properties as their polynomial counterparts. In this paper, we consider generalized spline spaces over planar T-meshes, and we deepen their parallelism with polynomial spline spaces over the same partitions. First, we extend the homological approach from polynomial to generalized splines. This provides some new insights into the dimension problem of a generalized spline space defined on a prescribed T-mesh for a given degree and smoothness. Second, we extend the construction of LR-splines to the generalized spline context.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.08.019