  We study the configuration space of rectangulations and convex subdivisions
of $n$ points in the plane. It is shown that a sequence of $O(n\log n)$
elementary flip and rotate operations can transform any rectangulation to any
other rectangulation on the same set of $n$ points. This bound is the best
possible for some point sets, while $\Theta(n)$ operations are sufficient and
necessary for others. Some of our bounds generalize to convex subdivisions of
$n$ points in the plane.
