**Abstract:**
We study two kinds of quasi-interpolants (abbr. QI) in the space of $C^2$ piecewise cubics
in the plane, or in a rectangular domain, endowed with the Powell-Sabin (PS) triangulation
generated by a uniform 6-direction mesh. It has been proved recently that this space is
generated by the integer translates of two multi-box splines. One kind of QIs is of
differential type and the other of discrete type. As those QIs are exact on the space of cubic
polynomials, their approximation order is 4 for sufficiently smooth functions. In addition,
they exhibit nice superconvergent properties at some specific points. Moreover, the infinite
norms of the discrete QIs being small, they give excellent approximations of a smooth function
and of its first order partial derivatives. The approximation properties of the QIs are
illustrated by numerical examples.

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