Moving a polygon around the corner in a corridor

We consider the problem of moving an <italic>n</italic> vertex simple polygon around a corner in a right-angular corridor. We give an <italic>&Ogr;</italic>(<italic>n</italic> log <italic>n</italic>) algorithm for a convex polygon which constructs a motion of the polygon when one exists; otherwise it reports that none exists. In the case of non-convex polygons, we have an <italic>&Ogr;</italic>(<italic>n</italic><supscrpt>2</supscrpt>) time algorithm.