  Given an $n$-vertex graph and two straight-line planar drawings of the graph
that have the same faces and the same outer face, we show that there is a morph
(i.e., a continuous transformation) between the two drawings that preserves
straight-line planarity and consists of $O(n)$ steps, which we prove is optimal
in the worst case. Each step is a unidirectional linear morph, which means that
every vertex moves at constant speed along a straight line, and the lines are
parallel although the vertex speeds may differ. Thus we provide an efficient
version of Cairns' 1944 proof of the existence of straight-line
planarity-preserving morphs for triangulated graphs, which required an
exponential number of steps.
