Handouts:
2/27/08: Final remarks about triangulations; Intro to convex hulls

I draw a Venn diagram showing simple polygons, monotone polygons, convex polygons, monotone mountains. (Can you add the star-shaped polygons to the Venn diagram?)

Summary: Simple polygons can be triangulated in time O(n), using Chazelle's (very complicated) algorithm; you are expected to know this exists, but we did not cover it. Polygons with holes (and also polygons without holes (simple polygons)) can be triangulated in time O(n log n), using the algorithm we have covered in class (Chapter 2).
LOWER BOUND: For the problem of triangulating a polygon with holes, Omega(n log n) is a lower bound; I sketch a bit of the proof (from SORTING, which I show also has an Omega(n log n) lower bound).
Introduction: definition of convex set, convex combinations, affine combinations, linear combinations. Examples of convex sets. Definition of convex hull. Equivalent characterizations of convex hulls.