Interpolation with quintic Powell–Sabin splines

We discuss local Hermite interpolation by C2 quintic Powell–Sabin splines represented in a normalized B-spline basis. We derive explicit formulae for the spline coefficients in this B-spline representation to interpolate given Hermite data. As part of the analysis, we show how tensor algebra can be used to describe polynomials in Bernstein–Bézier form and to simplify their manipulation.