How to Morph a Tree on a Small Grid

Fidel Barrera-Cruz; Manuel Borrazzo; Giordano Da Lozzo; Giuseppe Di Battista; Fabrizio Frati; Maurizio Patrignani; Vincenzo Roselli

arXiv · 1909.07093

How to Morph a Tree on a Small Grid

Fidel Barrera-Cruz·Manuel Borrazzo·Giordano Da Lozzo·Giuseppe Di Battista·Fabrizio Frati·Maurizio Patrignani·Vincenzo Roselli

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Abstract

In this paper we study planar morphs between straight-line planar 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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Fidel Barrera-Cruz, Manuel Borrazzo, Giordano Da Lozzo, Giuseppe Di Battista, Fabrizio Frati, Maurizio Patrignani, Vincenzo Roselli. 2019-09-16. How to Morph a Tree on a Small Grid. https://arxiv.org/abs/1909.07093

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