Before revision:  Recently, Chaplick et al.  introduced a different measure for the visual complexity, the affine cover number , which is the minimum number of lines (or planes) that together cover a  straight-line drawing of a graph G in 2D (3D).
After revision:  Recently, Chaplick et al. introduced a different measure for the visual complexity, the affine cover number , which is the minimum number of lines (or planes) that together cover a crossing-free straight-line drawing of a graph G in 2D (3D).