On Morphing 1-Planar Drawings

05/27/2021

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by   Patrizio Angelini, et al.

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Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of topology-preserving morphs for pairs of non-planar graph drawings. We make a step towards this problem by showing that a topology-preserving morph always exists for drawings of a meaningful family of 1-planar graphs. While our proof is constructive, the vertices may follow trajectories of unbounded complexity.