  In this work half-flat metrics are obtained from Hitchin's equations. The
SU$(\infty)$ Hitchin's equations are obtained and as a consequence of them, the
Husain-Park equation is found. Considering that the gauge group is SU$(2)$,
some solutions associated to Liouville, sinh-Gordon and Painlev\'e III
equations are taken and, through Moyal deformations, solutions of the
SU$(\infty)$ Hitchin's equations are obtained. From these solutions,
hamiltonian vector fields are determined, which in turn are used to construct
the half-flat metrics. Following an approach of Dunajski, Mason and Woodhouse,
it is also possible to construct half-flat metrics on ${\cal M}
\times\mathbb{CP}^{1}$.
