order of the edges incident to $u$ in $\Gamma$ is the same as the order associated to $u$ in $T$. Note that a strictly-upward drawing $\Gamma$ of an ordered rooted tree $T$ is order-preserving if and only if, for each node $u\in V(T)$, the edges from $u$ to its children enter $u$ in the left-to-right order associated with $u$.

The *bounding box* of a drawing $\Gamma$ is the smallest axis-parallel rectangle enclosing $\Gamma$. In a *grid* drawing $\Gamma$ each node has integer coordinates; then the *width* and the *height* of $\Gamma$, denoted by $w(\Gamma)$ and $h(\Gamma)$, respectively, are the number of grid columns and rows intersecting the bounding box of $\Gamma$, while the *area* of $\Gamma$ is its width times its height. For a node $v$ in a drawing $\Gamma$, an *$\ell$-box centered at $v$* is the convex hull of the square whose corners are $(x_\Gamma(v) \pm \frac{\ell}{2}, y_\Gamma(v) \pm \frac{\ell}{2})$.

#### Morphs.

A *morph* between two straight-line drawings $\Gamma_0$ and $\Gamma_1$ of a graph $G$ is a continuously changing family of drawings $\{\Gamma_t\}$ of $G$ indexed by time $t\in [0,1]$, such that the drawing at time $t=0$ is $\Gamma_0$ and the drawing at time $t=1$ is $\Gamma_1$. A morph 