  In this paper, we investigate crossing-free 3D morphs between planar
straight-line drawings. We show that, for any two (not necessarily
topologically equivalent) planar straight-line drawings of an $n$-vertex planar
graph, there exists a piecewise-linear crossing-free 3D morph with $O(n^2)$
steps that transforms one drawing into the other. We also give some evidence
why it is difficult to obtain a linear lower bound (which exists in 2D) for the
number of steps of a crossing-free 3D morph.
