an $n$-node tree, there is a planar morph with $\Theta(n)$ morphing steps between $\Gamma_0$ and $\Gamma_1$ such that each intermediate grid drawing has polynomial area, where the input size is again measured by $n$ and by the width and the height of $\Gamma_0$ and $\Gamma_1$.

The first algorithm uses recursion; namely, it eliminates a leaf in the tree, it recursively morphs the drawings of the remaining tree and it then reintroduces the removed leaf in suitable positions during the morph. The second algorithm morphs the given drawings by independently changing their $x$- and $y$-coordinates; this technique is reminiscent of a recent paper by Da Lozzo et al. [@DBLP:conf/gd/LozzoBFPR18]. Finally, the third algorithm scales the given drawings up in order to make room for a bottom-up modification of each drawing into a “canonical” drawing of the tree.

We remark that, although tree drawing algorithms are well investigated in Graph Drawing, morphs of tree drawings have not been the subject of research until now, with the exception of the recent work by Arseneva et al. [@DBLP:conf/gd/ArsenevaBCDDFLT18], who showed how to construct a three-dimensional crossing-free morph between two straight-line planar drawings of an $n$-node tree in $O(\log n)$ morphing steps.

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