We study the question whether a crossing-free 3D morph between two straight-line drawings of an $n$-vertex tree $T$ can be constructed consisting of a small number of linear morphing steps. We look both at the case in which the two given drawings are two-dimensional and at the one in which they are three-dimensional. In the former setting we prove that a crossing-free 3D morph always exists with $O({rpw}(T))subseteq O(log n)$ steps, where ${rpw}(T)$ is the rooted pathwidth or Strahler number of $T$, while for the latter setting $Theta(n)$ steps are always sufficient and sometimes necessary.
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机译：我们研究以下问题：是否可以由少量的线性变形步骤构成$ n $-顶点树$ T $的两条直线图形之间的无交叉3D变形。我们既查看两个给定附图均为二维的情况，又查看它们均为三维图的情况。在前一种设置中，我们证明了$ O（{rpw}（T）） subseteq O（ log n）$步长始终存在无交叉3D变形，其中$ {rpw}（T）$是根路径宽度或$ T $的Strahler数，而对于后者，设置$ Theta（n）$步长总是足够的，有时是必要的。
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