$S$ is the complement of the [Minkowski sum][1]${}^*$ of a connected body and the sphere of radius $r$.
${}^*$ Provided the Minkowski sum doesn't self-intersect. [1]: http://en.wikipedia.org/wiki/Minkowski_sum
$S$ is the complement of the [Minkowski sum][1]${}^*$ of a connected body and the sphere of radius $r$.
${}^*$ Provided the Minkowski sum doesn't self-intersect. [1]: http://en.wikipedia.org/wiki/Minkowski_sum