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.