Maintaining the extent of a moving point set

Let S be a set of it moving points in the plane. We give new efficient and compact kinetic data structures for maintaining the diameter, width, and smallest area or perimeter bounding rectangle of S. If the points in S move with algebraic motions, these structures process O(n(2+epsilon)) events. We also give constructions showing that Omega (n(2)) combinatorial changes are possible for these extent functions even if each point is moving with constant velocity. We give a similar construction and upper bound for the convex hull, improving known results.