If it is only necessary to determine the absolute maximum or absolute
minimum of the squared distance function between two geometric
objects, then simply computing the maximum or minimum of the set of
distances at the stationary points is sufficient, provided that this
set is finite. However, it is often necessary to classify each
stationary point as a local maximum, local minimum, or saddle point.
Furthermore, the set of stationary points may not be finite (for
example, consider the distance function between two concentric
circles) and it may be required to trace out these infinite point
sets. In this section we examine these questions.