Journal of Computational and Applied Mathematics ( IF 2.037 ) Pub Date : 2020-10-16 , DOI: 10.1016/j.cam.2020.113245
Jan Grošelj; Hendrik Speleers

Starting from a general B-spline representation for ${C}^{1}$ cubic Powell–Sabin splines on arbitrary triangulations, we focus on the construction of a B-spline representation for a particular subspace defined on three-directional triangulations with ${C}^{2}$ super-smoothness over each of the macro-triangles. We analyze the properties of the basis and point out the relation with simplex splines. Furthermore, we provide explicit expressions for the B-spline coefficients of any element of the spline space, and derive subdivision rules under dyadic refinement. Finally, we show simple conditions ensuring global ${C}^{2}$ smoothness on the domain.

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