In 1972, Sklansky presented  the first algorithm for finding the convex hull of a simple polygon in linear time. It is an extremely simple procedure. Even though it is wrong, the main step is used in many algorithms to follow, so I suggest understanding it.
This link provides detailed information on Sklansky's algorithm: 3 Coins algorithm.
Click here to go to Sklansky's second algorithm, which is based on this one (or just keep reading, you'll get to it).