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Simplex Spline Bases on the Powell-Sabin 12-Split: Part II
- Source :
- Multivariate Splines and Algebraic Geometry. Oberwolfach Report 12 (2015), Pages 1169 - 1172
- Publication Year :
- 2015
-
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 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.<br />Comment: Oberwolfach report for the conference Multivariate Splines and Algebraic Geometry
- Subjects :
- Mathematics - Numerical Analysis
41A15, 65D07, 65D17
Subjects
Details
- Database :
- arXiv
- Journal :
- Multivariate Splines and Algebraic Geometry. Oberwolfach Report 12 (2015), Pages 1169 - 1172
- Publication Type :
- Report
- Accession number :
- edsarx.1505.01801
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.4171/OWR/2015/21