Much study has been devoted to updating geometric structures as they
change over time.  Most of this research has concerned efficient
insertion and deletion of objects, but a recent paper [bgh-dsmd-97]
has developed {\em kinetic data structures} for problems such as the
convex hull and closest pair of points moving in the plane. These are
data structures that can be easily updated as objects move
continuously in space. In that paper, however, only worst-case
measures for these structures were derived, and these might not
reflect how the kinetic structures really perform in practice.  In
this paper, we study the data structures of [bgh-dsmd-97] and compare
them against alternative kinetic structures and other simple, brute
force methods.  We use this data to develop empirical bounds on the
performance of the kinetic data structures of [bgh-dsmd-97], verifying
that on a wide range of problems they are superior to alternative
approaches. We also address numerical robustness issues for kinetic
data structure implementation.