Recently there has been an issue come up from a few different people about the nature of ad orientem when a church is not oriented geographically East.
It made me realize this is probably a topic that should be quickly covered off in a main post, and not merely private email or in the comments.
The question is this: if we are looking at restoring ad orientem liturgies in a parish, what happens if the parish church's altar is not located at the Eastern end of the building?
The root of this question is a consideration of the practice in the early Church, which would typically either find the apse (sanctuary and altar) in the East -- toward which all would face -- or as in the case of some Roman basilicas, which were often westwardly oriented, where the faithful would all turn away from the altar to look East. So the question arises for some, "what happens if the Church is not oriented to the East, but North, South, or West?"
The answer to this question lay in the development of ad orientem which shifted away from the principle of geographical Eastwardness to liturgical (or symbolic) Eastwardness.
The primary symbolism of "turning East" was of the Christian community together turning towards the Lord.; this is what "the East" symbolized. It was a reference to the Second Coming of Christ in glory. It has eschatological and cosmological significance as a liturgical symbol.
Gradually (organically), the actual geographical orientation became less important than the symbolic significance and meaning found in the faithful and the priest being turned together in a common (sacred) direction. Thus, while the geographical aspect was lessened, the primary liturgical and theological symbol intended by the literal turning to the East was not.
Therefore, in answer to the original question, geographical orientation is not a necessary requirement of ad orientem as it has developed. Rather, it is manifest today in the symbolic, liturgical "Eastwardness" of the priest and faithful together facing in the same common direction. Besides the preservation of the primary symbol itself, this practice also has the same effect that would have been the result of all turning to the literal East; a common, united, sacred direction imbued with liturgical and theological meaning.