Handouts:
See the slides
3/11/09: Convex hulls in 2D: last remarks. Convex polytopes and convex hulls in 3 or more dimensions

The "ultimate convex hull algorithm" takes O(n log h) time (first shown by Kirkpatrick and Seidel, then drastically simplified by Timothy Chan), and there is a known lower bound of Omega(n log h), showing that this is the best you can do if the time bound is written both in terms of n and h.
Graduate students are expected to understand the algorithm; undergraduates are expected to know that it is possible, and this is the best bound achievable in terms of n and h.

Definition of convex polyhedron. (See Chapter 4, O'Rourke.)

Combinatorics: planar graphs, Euler's formula, linearity of the number of edges and faces (as a function of n, the number of vertices).

Discussion of Platonic Solids.

Introduction to convex hulls in 3 or more dimensions.

In 3D, the CH can be found using divide-and-conquer in time O(n log n). We state that the time it takes to compute a hull in d dimensions for d>=4 is O(n^{floor(d/2)}), which is the worst-case complexity of the output size (ie., the hull may have that many faces).