B-spline-like bases for $C^3$ quintics on the Powell-Sabin 12-split

Tom Lyche, Georg Muntingh

Published 2015-04-10Version 1

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, and domain points with an intuitive control net. 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.