  The Kirchhoff approximation (K-A) to calculate the acoustic backscattering of
a complex structure can be evaluated using a discretized version of its surface
(i.e. a $\textit{mesh}$). From the computational viewpoint, the most accesible
approach is the one based on flat facets. However, in the high frequency range,
where the K-A provides good agreement and is therefore applicable, it requires
a mesh with such a large number of facets that it turns impractical. To avoid
these difficulties a mesh of curved triangles can be used to model the
scatterer's complex structure. Previous computational implementations reported
in the literature did not accomplish satisfactory results for high frequency.
In this work we propose a numerical model based upon an iterative integration
using Gauss-Legendre rules. The model was validated against exact solutions and
led us to achieve adequate results in the high-frequency range.
