  Let $P : \Sigma \rightarrow S$ be a finite degree covering map between
surfaces. Rafi and Schleimer show that there is an induced quasi-isometric
embedding $\Pi : \mathcal{C}(S) \rightarrow \mathcal{C}(\Sigma)$ between the
associated curve complexes. We define an operation on curves in
$\mathcal{C}(\Sigma)$ using minimal intersection number conditions and prove
that it approximates a nearest point projection to $\Pi(\mathcal{C}(S))$. We
also approximate hulls of finite sets of vertices in the curve complex,
together with their corresponding nearest point projections, using intersection
numbers.
