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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Veröffentlicht in:Applied mathematics and computation Jg. 272; S. 187 - 198
Hauptverfasser: Bracco, Cesare, Lyche, Tom, Manni, Carla, Roman, Fabio, Speleers, Hendrik
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 01.01.2016
Schlagworte:
Dimension formula
Generalized splines
LR-meshes
T-meshes
Generalized splines
T-meshes
LR-meshes
Dimension formula
ISSN:0096-3003, 1873-5649
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Zusammenfassung: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