  We present a perfect simulation of the hard disks model via the partial
rejection sampling method. Provided the density of disks is not too high, the
method produces exact samples in $O(\log n)$ rounds, and total time $O(n)$,
where $n$ is the expected number of disks. The method extends easily to the
hard spheres model in $d>2$ dimensions. In order to apply the partial rejection
method to this continuous setting, we provide an alternative perspective of its
correctness and run-time analysis that is valid for general state spaces.
