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 \(O(\log n)\) steps, while for the latter \(\varTheta (n)\) steps are always sufficient and sometimes necessary.
We thank Therese Biedl for pointing out Remark 2. The research for this paper started during the Intensive Research Program in Discrete, Combinatorial and Computational Geometry, which took place in Barcelona, April-June 2018. We thank Vera Sacristán and Rodrigo Silveira for a wonderful organization and all the participants for interesting discussions.
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