Rather than trying to sample close to the boundary, another strategy
is to force the samples to be as far from the boundary as possible.
Let be a metric space. Let a *maximal ball* be a ball
such that no other ball can be a proper subset.
The centers of all maximal balls trace out a one-dimensional set of
points referred to as the *medial axis*. A simple example of a
medial axis is shown for a rectangular subset of
in Figure
5.30. The medial axis in
is based on the largest
balls that can be inscribed in
. Sampling on the
medial axis is generally difficult, especially because the
representation of
is implicit. Distance information from
collision checking can be used to start with a sample,
,
and iteratively perturb it to increase its distance from
[635,971]. Sampling on the
medial axis of
has also been proposed
[455]. In this case, the medial axis in
is easier to compute, and it can be used to heuristically guide the
placement of good roadmap vertices in
.

Steven M LaValle 2020-08-14