  Let $S$ be a set of $n$ points in general position in the plane. Join every
pair of points in $S$ with a straight line segment. Let $\overline{cr}(S)$ be
number of pairs of these edges that intersect in their interior. Suppose that
this number is known. In this paper we consider the problem of computing
$\overline{cr}(S')$, where $S'$ comes from adding, deleting or moving a point
from $S$.
