Weil (1995) defined a convexification operation
for windows $W$ that belong to the convex ring (that is,
for any $W$ which is a finite union of convex sets).
Note that this is not the same as the convex hull. The convexified set $f(W)$ has the same total boundary length as
$W$ and the same distribution of orientations of the boundary.
If $W$ is a polygonal set, then the convexification $f(W)$
is obtained by rearranging all the edges of $W$ in order of
their spatial orientation.
The argument W must be a window. If it is not already a polygonal
window, it is first converted to one, using
simplify.owin.
The edges are sorted in increasing order of angular orientation
and reassembled into a convex polygon.