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(logn) steps, while for the latter Θ(n) steps are always sufficient and sometimes necessary.
Cite
@article{arxiv.1808.10738,
title = {Pole Dancing: 3D Morphs for Tree Drawings},
author = {Elena Arseneva and Prosenjit Bose and Pilar Cano and Anthony D'Angelo and Vida Dujmovic and Fabrizio Frati and Stefan Langerman and Alessandra Tappini},
journal= {arXiv preprint arXiv:1808.10738},
year = {2018}
}
Comments
Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018)