  In this paper, the construction of $C^{1}$ cubic quasi-interpolants on a
three-direction mesh of $\RR^{2}$ is addressed. The quasi-interpolating splines
are defined by directly setting their Bernstein-B\'{e}zier coefficients
relative to each triangle from point and gradient values in order to reproduce
the polynomials of the highest possible degree. Moreover, additional global
properties are required. Finally, we provide some numerical tests confirming
the approximation properties.
