Convexification of polygons by flips and by flipturns (Q5951945)

The authors generalize the known result that every simple polygon can be convexified by a finite number of flips, or of flipturns, to the following class of more general polygons: A polygon is a sequence of \(n \geq 2\) points \(V_i\) in the Euclidean plane and closed segments \(V_iV_{i+1}\) with \(V_{n+1}=V_1\) and \(V_i \neq V_{i+1}\) for all \(i\). NEWLINENEWLINENEWLINEThe result of the convexification, obviously, is only a ``weakly convex'' or a ``nearly convex'' polygon which is contained in the boundary of its convex hull or which is a subdivision of a segment.