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arXiv · 1808.10738

Pole Dancing: 3D Morphs for Tree Drawings

Elena Arseneva·Prosenjit Bose·Pilar Cano·Anthony D'Angelo·Vida Dujmovic·Fabrizio Frati·Stefan Langerman·Alessandra Tappini
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Abstract

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 $\Theta(n)$ steps are always sufficient and sometimes necessary.

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Elena Arseneva, Prosenjit Bose, Pilar Cano, Anthony D'Angelo, Vida Dujmovic, Fabrizio Frati, Stefan Langerman, Alessandra Tappini. 2018-08-31. Pole Dancing: 3D Morphs for Tree Drawings. https://arxiv.org/abs/1808.10738

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