  Given a drawing of a graph, its \emph{visual complexity} is defined as the
number of geometrical entities in the drawing, for example, the number of
segments in a straight-line drawing or the number of arcs in a circular-arc
drawing (in 2D). Recently, Chaplick et al. [GD 2016] introduced a different
measure for the visual complexity, the \emph{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). In this paper, we introduce
the \emph{spherical cover number}, which is the minimum number of circles (or
spheres) that together cover a crossing-free circular-arc drawing in 2D (or
3D). It turns out that spherical covers are sometimes significantly smaller
than affine covers. Moreover, there are highly symmetric graphs that have
symmetric optimum spherical covers but apparently no symmetric optimum affine
cover. For complete, complete bipartite, and platonic graphs, we analyze their
spherical cover numbers and compare them to their affine cover numbers as well
as their segment and arc numbers. We also link the spherical cover number to
other graph parameters such as chromatic number, treewidth, and linear
arboricity.
