Summary of Generation of
Simple Polygons
Details presented in class
Humans vs. Machines
• The task of generating a simple polygon from a set of n points in the
plane has been described.
• Humans do so flawlessly.
• However, we do not know how we perform this task.
• There are many other tasks which humans can do well and extremely
fast including patterns recognition, clustering, …
• However, to turn our human knowledge into algorithms remains
tough.
Algorithmic solutions
• We studied (in class) attempts to translate human approaches into
algorithms but saw the difficulty.
• We then studied two algorithms for solving the problem of generating a
simple polygon from an input set of n points in the plane.
• These approaches take O(n log n) time and generate specific classes of
simple polygons, namely star-shaped and monotone polygons. (see class)
• Thus, they are not well suitable to generate more “unstructured” simple
polygons and subsequent algorithms may exploit the structure.