Pole dancing: 3D morphs for tree drawings

We study the question whether a crossing-free 3D morph between two straight-line drawings of an n-vertex tree 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)) ⊆ O(log n) steps, while for where rpw(T) is the rooted pathwidth or Strahler number of T, while for the latter setting Θ(n) steps are always sufficient and sometimes necessary.

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