  We prove that circle graphs (intersection graphs of circle chords) can be
embedded as intersection graphs of rays in the plane with polynomial-size bit
complexity. We use this embedding to show that the global curve simplification
problem for the directed Hausdorff distance is NP-hard. In this problem, we are
given a polygonal curve $P$ and the goal is to find a second polygonal curve
$P'$ such that the directed Hausdorff distance from $P'$ to $P$ is at most a
given constant, and the complexity of $P'$ is as small as possible.
