Abstract
In this paper we study planar morphs between planar straight-line grid drawings of trees. A morph consists of a sequence of morphing steps, where in a morphing step vertices move along straight-line trajectories at constant speed. We show how to construct planar morphs that simultaneously achieve a reduced number of morphing steps and a polynomially-bounded resolution. We assume that both the initial and final drawings lie on the grid and we ensure that each morphing step produces a grid drawing; further, we consider both upward drawings of rooted trees and drawings of arbitrary trees.
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Notes
When applying Lemma 4.4 in order to transform a canonical drawing of a subtree of T into another canonical drawing of the same subtree of T, we sometimes informally refer to such a transformation as a “rotation”. However, the transformation obtained by means of Lemma 4.4 is a linear morph, and not a rotation. The reason for using the term “rotation” is that the final (canonical) drawing of the morph is the same as the one that we would get by applying an actual \(90^\circ \)-rotation to the initial (canonical) drawing.
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This research was supported in part by MIUR Project “AHeAD” under PRIN 20174LF3T8 and by H2020-MSCA-RISE project 734922—“CONNECT”
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Barrera-Cruz, F., Borrazzo, M., Da Lozzo, G. et al. How to Morph a Tree on a Small Grid. Discrete Comput Geom 67, 743–786 (2022). https://doi.org/10.1007/s00454-021-00363-8
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DOI: https://doi.org/10.1007/s00454-021-00363-8