Quartic splines on Powell–Sabin triangulations

The paper deals with the construction of bivariate quartic splines on Powell–Sabin triangulations. In particular, it provides a spline space that is C2 everywhere except across some edges of the refined triangulation. The splines that belong to this space can be described uniquely with interpolation...

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Bibliographic Details
Published in:Computer aided geometric design 2016-12, Vol.49, p.1-16
Main Authors: Grošelj, Jan, Krajnc, Marjeta
Format: Article
Language:English
Subjects:
Normalized B-splines
Powell–Sabin triangulation
Quartic splines
Quasi-interpolants
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Summary:The paper deals with the construction of bivariate quartic splines on Powell–Sabin triangulations. In particular, it provides a spline space that is C2 everywhere except across some edges of the refined triangulation. The splines that belong to this space can be described uniquely with interpolation values and derivatives of order at most two. Moreover, they can be represented in a locally supported basis that forms a convex partition of unity. As an application of this result, quasi-interpolants that reproduce polynomials of degree four are derived. •Bivariate quartic splines on Powell–Sabin triangulations are considered.•Local B-spline basis that forms a convex partition of unity is derived.•Properties and calculation of the B-spline representation are discussed.•Quasi-interpolants relying on the derived B-splines are presented.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2016.10.001