  A morph between two straight-line planar drawings of the same graph is a
continuous transformation from the first to the second drawing such that
planarity is preserved at all times. Each step of the morph moves each vertex
at constant speed along a straight line. Although the existence of a morph
between any two drawings was established several decades ago, only recently it
has been proved that a polynomial number of steps suffices to morph any two
planar straight-line drawings. Namely, at SODA 2013, Alamdari et al.[1] proved
that any two planar straight-line drawings of a planar graph can be morphed in
O(n^4) steps, while O(n^2) steps suffice if we restrict to maximal planar
graphs.
  In this paper, we improve upon such results, by showing an algorithm to morph
any two planar straight-line drawings of a planar graph in O(n^2) steps;
further, we show that a morph with O(n) steps exists between any two planar
straight-line drawings of a series-parallel graph.
