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A normalized representation of super splines of arbitrary degree on Powell–Sabin triangulations

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Abstract

In the paper, a family of bivariate super spline spaces of arbitrary degree defined on a triangulation with Powell–Sabin refinement is introduced. It includes known spaces of arbitrary smoothness r and degree \(3r-1\) but provides also other choices of spline degree for the same r which, in particular, generalize a known space of \(\mathscr {C}^{1}\) cubic super splines. Minimal determining sets of the proposed super spline spaces of arbitrary degree are presented, and the interpolation problems that uniquely specify their elements are provided. Furthermore, a normalized representation of the discussed splines is considered. It is based on the definition of basis functions that have local supports, are nonnegative, and form a partition of unity. The basis functions share numerous similarities with classical univariate B-splines.

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Authors and Affiliations

  1. FMF, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Jan Grošelj

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  1. Jan Grošelj
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Correspondence to Jan Grošelj.

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Communicated by Tom Lyche.

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Grošelj, J. A normalized representation of super splines of arbitrary degree on Powell–Sabin triangulations. Bit Numer Math 56, 1257–1280 (2016). https://doi.org/10.1007/s10543-015-0600-y

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  • DOI: https://doi.org/10.1007/s10543-015-0600-y

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