The Convexification Algorithm
Traverse the polygon in the
direction it is oriented. When you
come to a turn:
• if the turn is a RHT, do nothing
• if the turn is a LHT, swap the
edges and continue
Theorem: The Convexification
Algorithm will convexify any
The Idea of the Proof:
Show that any two edges
of any star-shaped
polygon will be swapped
at most once.
let P be a clockwise-oriented, star-shaped
let a and b be edges of P which are adjacent.
let k be a point in the kernel of P.
let L be a line through k, and parallel to a.