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A crossing-free morph is a continuous deformation between two graph drawingsthat preserves straight-line pairwise noncrossing edges. Motivated byapplications in 3D morphing problems, we initiate the study of morphing graphdrawings in the plane in the presence of stationary point obstacles, which needto be avoided throughout the deformation. As our main result, we prove that itis NP-hard to decide whether such an obstacle-avoiding 2D morph between twogiven drawings of the same graph exists. This is in sharp contrast to theclassical case without obstacles, where there is an efficiently verifiable(necessary and sufficient) criterion for the existence of a morph.

Morphing Graph Drawings in the Presence of Point Obstacles