Simplex Spline Bases on the Powell-Sabin 12-Split: Part II
| Autor: | Lyche, Tom, Muntingh, Georg |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Multivariate Splines and Algebraic Geometry. Oberwolfach Report 12 (2015), Pages 1169 - 1172 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4171/OWR/2015/21 |
| Popis: | 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 B\'ezier 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. Comment: Oberwolfach report for the conference Multivariate Splines and Algebraic Geometry |
| Databáze: | arXiv |
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