Superconvergent quadratic spline quasi-interpolants on Powell-Sabin partitions

In this paper we use Normalized Powell-Sabin B-splines constructed by Dierckx [6] to introduce a new B-spline representation of Hermite Powell-Sabin interpolant of any polynomial or any piecewise polynomial over Powell-Sabin partitions of class at least C1 in terms of their polar forms. We use this representation for constructing several superconvergent discrete quasi-interpolants. The result that we present in this paper is a generalization of the one presented in [20] with other properties.