  In a Lombardi drawing of a graph the vertices are drawn as points and the
edges are drawn as circular arcs connecting their respective endpoints.
Additionally, all vertices have perfect angular resolution, i.e., all angles
incident to a vertex $v$ have size $2\pi/\mathrm{deg}(v)$. We prove that it is
$\exists\mathbb{R}$-complete to determine whether a given graph admits a
Lombardi drawing respecting a fixed cyclic ordering of the incident edges
around each vertex. In particular, this implies NP-hardness. While most
previous work studied the (non-)existence of Lombardi drawings for different
graph classes, our result is the first on the computational complexity of
finding Lombardi drawings of general graphs.
