A normalized basis for condensed C1C1 Powell–Sabin-12 splines

• B-spline basis of the quadratic condensed Powell–Sabin-12 spline space.
• Determination of control points.
• Discrete and differentiable quasi-interpolants.

The purpose of this article is the construction of a normalized basis for a quadratic condensed Powell–Sabin-12 macro-element space introduced by Alfeld et al. (2010). The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction of this basis is adopted from Dierckx (1997) and Speleers (2010a), and is based on the determination of a set of triangles that must contain a specific set of points. The proposed basis can only be constructed on triangulations with a maximal angle less than π2.