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- W1551972140 abstract "For the space $mathcal{S}$ of $C^3$ quintics on the Powell-Sabin 12-split of a triangle, we determine the simplex splines in $mathcal{S}$ and the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a positive partition of unity, a (barycentric) Marsden identity, and domain points with an intuitive control net. We provide a quasi-interpolant with approximation order 6 and a Lagrange interpolant at the domain points. The latter can be used to show that each basis is stable in the $L_infty$ norm, which yields an $h^2$ bound for the distance between the Bezier ordinates and the values of the spline at the corresponding domain points. Finally, for one of these bases we provide $C^0$, $C^1$, and $C^2$ conditions on the control points of two splines on adjacent macrotriangles, and a conversion to the Hermite nodal basis." @default.
- W1551972140 created "2016-06-24" @default.
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- W1551972140 date "2015-05-07" @default.
- W1551972140 modified "2023-09-27" @default.
- W1551972140 title "Simplex Spline Bases on the Powell-Sabin 12-Split: Part II" @default.
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- W1551972140 hasPublicationYear "2015" @default.
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