Superconvergent trivariate quadratic spline quasi-interpolants on Worsey–Piper split

In this paper we use Normalized trivariate Worsey–Piper B-splines recently constructed by Sbibih et al. (2012) and the method proposed in Sbibih et al. (2013) to give a new representation of Worsey–Piper Hermite interpolant of any piecewise polynomial of class at least C1C1 over the Worsey–Piper split in terms of its polar forms. Using this representation we construct several superconvergent discrete quasi-interpolants. The construction that we present in this work is a generalization of the one presented in Sbibih et al. (2012) with other properties.