How to Morph a Tree on a Small Grid

TL;DR

This paper presents a method for smoothly transforming tree drawings on a grid with minimal steps and high resolution, ensuring planarity and grid adherence throughout the morph.

Contribution

It introduces a construction for planar morphs of tree drawings that minimizes steps and maintains polynomial resolution, applicable to both rooted and arbitrary trees.

Findings

Achieves fewer morphing steps while maintaining planarity.

Ensures each intermediate drawing remains on the grid.

Applicable to both upward and arbitrary tree drawings.

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.