We introduce endpoint projection (EPP), a translation of choreographies into implementations given in terms of compositions of processes. Endpoint projection is proven to guarantee choreography compliance by establishing a correspondence between the semantics of source choreographies and their corresponding implementations returned by EPP for them. Choreographies can be seen as descriptions of desired emergent behaviour for communicating processes. Endpoint projection is a way to obtain processes that will collectively implement the desired emergent behaviour. Building on the correctness of EPP and the properties of choreographies, we prove that the implementations generated by EPP are always communication-safe and starvation-free.