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Stable simplex spline bases for $C^3$ quintics on the Powell-Sabin 12-split by Lyche, Tom; Muntingh, Georg is a scholarly article available to read on EtoBox.

What is Stable simplex spline bases for $C^3$ quintics on the Powell-Sabin 12-split about?

For the space of $C^3$ quintics on the Powell-Sabin 12-split of a triangle, we determine explicitly the six symmetric simplex spline bases that reduce to a B-spline basis on each edge, have a positive partition of unity, a Marsden identity that splits into real linear factors, and an intuitive domain mesh. The bases are stable in the $L_\infty$ norm with a condition number independent of the geometry, have a well-conditioned Lagrange interpolant at the domain points, and a quasi-interpolant with local approximation order 6. We show an $h^2$ bound for the distance between the control points and the values of a spline at the corresponding domain points. For one of these bases we derive $C^0$, $C^1$, $C^2$ and $C^3$ conditions on the control points of two splines on adjacent macrotriangles.

Author

Lyche, Tom; Muntingh, Georg

Published

2015

Language

EN