Unbent collections of non-planar $s$-grid-drawing

In a recent paper, Antić et al.~studied collections of planar orthogonal drawings of a graph where every edge is unbent in at least one drawing.

This paper generalizes this concept to non-planar drawings, and shows that then two drawings always suffice (for planar drawings three drawings are sometimes needed).

The results can also be generalized to $s$-grid drawings for $s\geq 3$.