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.

Journal of Graph Algorithms and Applications
School of Computer Science

Arseneva, E. (Elena), Bose, P, Cano, P. (Pilar), D’Angelo, A. (Anthony), Dujmović, V, Frati, F. (Fabrizio), … Tappini, A. (Alessandra). (2019). Pole dancing: 3D morphs for tree drawings. Journal of Graph Algorithms and Applications, 23(3), 579–602. doi:10.7155/jgaa.00503