On the choice of the PS-triangles

n this paper we look at different bases for the space S^1_2(Δ_PS) of C^1 continuous quadratic splines on Powell-Sabin triangle splits. First, by requiring a partition of unity, we describe a general framework that leads to the notion of PS-triangles and control triangles. This is a useful property that gives insight in the shape of the surface. The problem of choosing appropriate basis functions for a certain triangulation of the domain is now equivalent to choosing the corresponding PS-triangles. Then we consider two choices more in detail: a normalised B-spline basis, and a basis based on minimal determining sets. The approach with minimal determining sets leads to bases that are stable as a function of the smallest angle in the triangulation. The basis functions are not only linearly independent but also locally linearly independent. In the normalised B-spline representation the basis functions form a convex partition of unity. Geometrically this can be interpreted as a PS-triangle containing a specific set of Bézier domain points. There is more than one triangle that satisfies this requirement. We show why the triangle with minimal area is a suitable choice and also give an alternative that is computationally more efficient.nrpages: 14status: publishe