Norsk English

Stable Simplex Spline Bases for C3 Quintics on the Powell–Sabin 12-Split

Abstract

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 and 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 and 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.

Client

• Research Council of Norway (RCN) / 222335

English

Affiliation

• University of Oslo
• SINTEF Digital / Mathematics and Cybernetics

2016

Published in

Constructive approximation

0176-4276

Springer

45

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