Moviegoers enjoying Saturday Night Fever on the lawn in Bryant Park at the HBO Bryant Park Summer Film Festival are probably not reflecting on the long history of this plot, behind the New York Public Library on West 42nd Street. In the 1820s and 1830s, it was the city’s potter’s field, which was moved to Randalls Island in 1840 and then to Hart Island. It became a park in 1847, and hosted the city’s first world’s fair six years later. In more recent times, it was a troubled, and at times dangerous, place that was rescued in 1992 by a thoughtful and innovative plan that has led to its renaissance as a popular gathering place.