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.

dx.doi.org/10.7155/jgaa.00503
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