A normalized basis for C1 cubic super spline space on Powell-Sabin triangulation

In this paper, we describe the construction of a suitable normalized B-spline representation for bivariate C^1 cubic super splines defined on triangulations with a Powell-Sabin refinement. The basis functions have local supports, they form a convex partition of unity, and every spline is locally controllable by means of control triangles. As application, discrete and differential quasi-interpolants of optimal approximation order are developed and numerical tests for illustrating theoretical results are presented.

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