Geodesic
Pole Dancing: 3D Morphs for Tree Drawings
Journal of Graph Algorithms and Applications, Special issue on Selected papers from the Twenty-sixth International Symposium on Graph Drawing and Network Visualization, GD 2018 , Tome 23 (2019) no. 3, pp. 579-602.

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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.
DOI : 10.7155/jgaa.00503
Keywords: graph drawing, morph, crossing-free 3D drawing, straight-line drawing, tree drawing 
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     author = {Elena Arseneva and Prosenjit Bose and Pilar Cano and Anthony D'Angelo and Vida Dujmovi\'c and Fabrizio Frati and Stefan Langerman and Alessandra Tappini},
     title = {Pole {Dancing:} {3D} {Morphs} for {Tree} {Drawings}},
     journal = {Journal of Graph Algorithms and Applications},
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%A Stefan Langerman
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Elena Arseneva; Prosenjit Bose; Pilar Cano; Anthony D'Angelo; Vida Dujmović; Fabrizio Frati; Stefan Langerman; Alessandra Tappini. Pole Dancing: 3D Morphs for Tree Drawings. Journal of Graph Algorithms and Applications, 
							Special issue on Selected papers from the Twenty-sixth International Symposium on Graph Drawing and Network Visualization, GD 2018
					, Tome 23 (2019) no. 3, pp. 579-602. doi : 10.7155/jgaa.00503. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00503/

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