  We find a compactification of the $\mathrm{SL}(3,\mathbb{R})$-Hitchin
component by studying the degeneration of the Blaschke metrics on the
associated equivariant affine spheres. In the process, we establish the closure
in the space of projectivized geodesic currents of the space of flat metrics
induced by holomorphic cubic differentials on a Riemann surface.
