Optimal Morphs of Convex Drawings

TL;DR

This paper presents an algorithm for morphing between convex drawings of the same plane graph, ensuring convexity preservation and linear complexity in vertex movement, with optimal worst-case bounds.

Contribution

It introduces an optimal algorithm for convex graph morphing that maintains convexity and achieves linear complexity in vertex trajectories.

Findings

Morph preserves convexity at all times

Vertex movements are piecewise linear with linear complexity

Algorithm is asymptotically optimal in worst-case complexity

Abstract

We give an algorithm to compute a morph between any two convex drawings of the same plane graph. The morph preserves the convexity of the drawing at any time instant and moves each vertex along a piecewise linear curve with linear complexity. The linear bound is asymptotically optimal in the worst case.