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

Projections in the curve complex arising from covering maps