  The affine sphere construction gives, on any oriented surface, a one-to-one
correspondence between convex $\mathbb{RP}^2$-structures and holomorphic cubic
differentials. Generalizing results of Benoist-Hulin, Loftin and Dumas-Wolf, we
show that poles of order less than $3$ of cubic differentials correspond to
finite volume ends of convex $\mathbb{RP}^2$-structures, and poles of order $3$
(resp. bigger than $3$) correspond to geodesic (resp. piecewise geodesic) ends.
In particular, at a pole of order at least $3$, we bordify the surface by
attaching to it a boundary circle in a natural way with respect to the cubic
differential, and show that the $\mathbb{RP}^2$-structure extends to the
boundary in a metric preserving way.
