Morphing Planar Graph Drawings Through 3D

Abstract

. In this paper, we investigate crossing-free 3D morphs between planar straight-line drawings. We show that, for any two (not necessarily topologically equivalent) planar straight-line drawings of an n -vertex planar graph, there exists a piecewise-linear crossing-free 3D morph with O ( n 2 ) steps that transforms one drawing into the other. We also give some evidence why it is difficult to obtain a linear lower bound (which exists in 2D) for the number of steps of a crossing-free 3D morph.