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A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin Triangulations

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Abstract

We investigate the construction of local quasi-interpolation schemes based on a family of bivariate spline functions with smoothness \(r\ge 1\) and polynomial degree \(3r-1\). These splines are defined on triangulations with Powell–Sabin refinement, and they can be represented in terms of locally supported basis functions that form a convex partition of unity. With the aid of the blossoming technique, we first derive a Marsden-like identity representing polynomials of degree \(3r-1\) in such a spline form. Then we present a general recipe to construct various families of smooth quasi-interpolation schemes involving values and/or derivatives of a given function.

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Authors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, 3001 , Leuven, Belgium

    Hendrik Speleers

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  1. Hendrik Speleers
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Correspondence to Hendrik Speleers.

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Communicated by Larry Schumaker.

H. Speleers is a Postdoctoral Fellow of the Research Foundation Flanders (Belgium).

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Speleers, H. A Family of Smooth Quasi-interpolants Defined Over Powell–Sabin Triangulations. Constr Approx 41, 297–324 (2015). https://doi.org/10.1007/s00365-014-9248-0

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  • DOI: https://doi.org/10.1007/s00365-014-9248-0

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