2014
DOI: 10.1016/j.matcom.2013.04.020
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A normalized basis for cubic super spline space on Powell–Sabin triangulation

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Cited by 23 publications
(11 citation statements)
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“…It extends the representation for S 1 2 ( * ) given in [3] and the representation for S 2,3 5 ( * ) presented in [16]. Recently, a similar construction for S 1,2 3 ( * ) was derived in [10]. In this section, these results are extended to a normalized representation for S d ( * ) with arbitrary d ∈ N, and its main properties are proved.…”
Section: A Normalized Representation Of Super Splinesmentioning
confidence: 55%
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“…It extends the representation for S 1 2 ( * ) given in [3] and the representation for S 2,3 5 ( * ) presented in [16]. Recently, a similar construction for S 1,2 3 ( * ) was derived in [10]. In this section, these results are extended to a normalized representation for S d ( * ) with arbitrary d ∈ N, and its main properties are proved.…”
Section: A Normalized Representation Of Super Splinesmentioning
confidence: 55%
“…Similarly as in [24] for d = 2, polynomial splines of arbitrary degree d can be generalized to rational splines. In [9,10,18] quasi-interpolants for splines of degrees 3 and 3r − 1, r ∈ N, were studied. These results can also be adapted for general degree.…”
Section: Resultsmentioning
confidence: 99%
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“…Recently, basis functions with similar properties have been constructed for certain Powell-Sabin spline spaces of higher degree and smoothness. In particular, we mention C 1 cubics (Lamnii et al, 2014), C 2 quintics (Speleers, 2010a), and a family of splines of smoothness r and polynomial degree 3r − 1 (Speleers, 2013a). Local super-smoothness has been imposed in order to simplify their construction and to reduce their number of degrees of freedom while maintaining the full order of approximation.…”
Section: Introductionmentioning
confidence: 99%