The need for analyzing and processing massive data in real time has led to a flurry of activity related to performing computations on a \emph{data stream}. In this paper we propose algorithms for computing extent measures and approximate representations of a stream of points in or . In particular, we study the problems of computing various extent measures (e.g.\ diameter, width, smallest enclosing rectangle, smallest enclosing disk) and of approximating a set of points by a circle or a line. We show that these problems can be solved efficiently using graphics hardware even in the streaming model. For example, we show that the diameter and width of a point set in can be approximated by making six passes over the data, and the smallest disk (resp.\ rectangle) containing a set of points in by making one pass (resp.\ four passes).
Our empirical study, which compares our algorithms to existing implementations for extent problems, shows that in many cases, our algorithm is considerably faster than the existing ones for the same level of accuracy. Our graphics-hrdware based technique can be used to solve a number of other geometric optimization problems, e.g., layered manufacturing, Hausdorff distance, which do not necessarily arise in the streaming model.