Schedule (rough: expect impromptu changes)

Week Lecture Topic
  CONVEX HULLS ALGORITHMS [BKOS00, Chapter 1]  
Week 1 Introduction, syllabus, course structure, etc. Computational problems, Algorithms, asymptotic complexity measures; Begin Convex Hulls; Convexity; Intuitive algorithms. Orientation test; Jarvis' march [J73 pdf ] Graham's scan [G72, pdf1 pdf2 A79]
Week 2 Convex hulls
Details: Divide & conquer; Chan's alg.[C96], Membership of point in convex region; Dynamic hull maintanence.
Week 2 Convex hulls
Lower bounds and close relationship to sorting; Reductions; Extreme Point problem and its relation to Convex Hull; How geometrization of combinatorial problems helps in proving lower bounds.
Week 3 Geometrization of Element Distinctness and Extreme Point and proving lower bounds for both
Week 3 Relationships between Membership (of point in region), Intersection (of 2 regions), Subdivision (of region into subregions), Pointset Partition, Point location (of point in subdivision); Membership in convex and starshaped polygons.
  PLANE-SWEEP ALGORITHMS [BKOS00, Chapters 2 and 3 ]  
Week 4 Line segment intersections
Plane-sweep [BO79]; membership in simple polygons.
Week 4 TEST 1
Week 5 Polygon Triangulation
Triangulating monotone polygons [GJPT78] Partitioning simple polygons
Week 5 Convex Partitioning
Lower and upper bounds, A factor 4 approximation algorithm
  LINEAR PROGRAMMING [BKOS00, Chapter 4 ]  
Week 6 Manufacturing with Molds
Necessary and Sufficient condition, Half-Plane Intersections
Week 6 Linear Programming
Feasible Region, Optimal solution;
Incremental and randomized algorithms
TITLE/TOPIC OF FINAL PROJECT DUE
  ORTHOGONAL SEARCH [BKOS00, Chapters 5 and 10]  
Week 7 Geometric data structures; Range search
Quad-tree; kd-tree [B75];
Week 7 Improvements on range searching
Range tree; fractional cascading [CG86]
Week 8 Inverse Range Search
Segment tree [B77]; interval tree [E83]; priority search tree [M85]
Week 8 TEST 2
  VORONOI DIAGRAMS & DELAUNAY TRIANGULATIONS
[BKOS00, Chapters 7, 9, and 14] 		 
Week 9 Voronoi diagrams
Voronoi diagrams [AK00]; furthest point Voronoi diagram, Other distance metrics
Week 9 Voronoi diagrams
Fortune's plane sweep algorithm
FIRST DRAFT OF FINAL PROJECT DUE
Week 10 Delaunay triangulation
Empty circles, local Delaunayhood [D34],
edge-flip [L77], lifting, analysis, maxmin angles
Week 10 Randomized incremental algorithm
Incremental construction [GKS92]; backward analysis [S93] Relating Voronoi diagrams to Convex hull (unifying geometric problems and algorithms using duality and arrangements).
Week 11 (possible that we move to ARRANGEMENTS already this week) Point Location
DAG structure for point location in triangulations
[BKOS00, Chapters 6 and 9]
Steiner triangulations
Steiner triangulation [BE95]; quality measure; quad-trees [BE95];
Week 11 Delaunay refinement
Circumcenter insertion [R95]; Sphere packing argument
  ARRANGEMENTS (possible that we use the previous week for this as well) [BKOS00, Chapter 8]  
Week 12 Zones
Duality; line arrangements; complexity;
incremental algorithm; zone theorem [ESS93]
Week 12 Levels and discrepancy
Geometric sampling, epsilon nets, VC dimension
Week 13 More on arrangements, duality, sampling
Week 13 TEST 3
  OTHER APPLICATIONS [BKOS00, Chapters 13 and 15]  
Week 14 Geometric Approximation Algorithms
TSP, Metric TSP, Euclidean TSP
Polynomial Time Approximation Scheme (PTAS)
Week 14 THANKSGIVING
Week 15 Geometrization and its uses
Week 15 Embedding algorithms, Distance geometry, combinatorial rigidity
Week 16 Term Paper Due

References

Books
[BKOS00] M. de Berg, M. van Kreveld, M. Overmars, and O. Schwarzkopf. Computational Geometry: Algorithms and Applications. Springer-Verlag, 3rd edition, 2008. [course textbook]
Lecture Slides by Marc van Kreveld (one of the authors of the textbook)
Intro Lecture with Line Segment Intersection
Lecture on Subdivision Overlays
Lecture on Polygon Triangulations
Lecture on Casting Polyhedra
Lecture on KD Trees
Lecture on Range Trees
Lecture on Window Queries
Lecture II on Window Queries
Point Location
Neighborhoods
Lecture on Voronoi
More Voronoi
Lecture II on Voronoi
Lecture on Delaunay
Arrangements
Lecture on Mesh Generation
Lecture on TSP slides
Lecture Slides by Subhash Suri
Lecture on Convex Hulls
Intro lecture
Closest Pair
Line Intersection
Triangulation and Shortest Paths
Range Searching
Point Location
Voronoi Diagrams and Delaunay
Sampling, Epsilon nets, VC dimension
Surveys
[E02] Lecture Notes on ConvexHulls by J. Erickson.
[E07] Lecture Notes on Polygon Triangulations by J. Erickson.
[BE95] M. Bern and D. Eppstein. Mesh generation and optimal triangulation. Computing in Euclidean Geometry (2nd ed.), D.-Z. Du and F. Hwang (eds.), World Scientific, 1995, 47-123.
[E00] H. Edelsbrunner. Triangulations and meshes in computational geometry. Acta Numerica (2000), 133-213.

Other Papers
[A79] A. M. Andrew. Another efficient algorithm for convex hulls in two dimensions. Information Processing Letters, 9:216-219, 1979. [A left-to-right variant of Graham's scan]
[AK00] F. Aurenhammer and R. Klein. Voronoi Diagrams. Handbook of Computational Geometry, Ed. J. Sack, J. Urrutia (eds.), 2000, 201-290.
[BDH96] B. Barber, D. Dobkin, and H. Huhdanpaa. The Quickhull Algorithm for Convex Hulls. ACM Transactions on Mathematical Software Vol. 22, No. 4, December 1996, Pages 469?483.
[B75] J. L. Bentley. Multidimensional binary search trees used for associative searching. Commun. ACM, 18:509-517, 1975.
[B77] J. L. Bentley. Solution to Klee's rectangle problems. Tech. Rep., Carnegie-Mellon Univ., Pittsburgh, 1975.
[BO79] J. L. Bentley and T. A. Ottmann. Algorithms for reporting and counting geometric intersections. IEEE Transactions on Computers, C-28:643-647, 1979.
[C96] T. Chan. Optimal output-sensitive convex hull algorithms in two and three dimensions. Discrete and Computational Geometry, 16:361-368, 1996.
[CE92] B. Chazelle and H. Edelsbrunner. An optimal algorithm for intersecting line segments in the plane. Journal of the ACM 39:1-54, 1992.
[CG86] B. Chazelle and L. J. Guibas. Fractional cascading. Algorithmica 1:133-162 and 163-191, 1986.
[D34] B. N. Delaunay. Sur la Sphere vide. Izvestia Akademia Nauk SSSR, VII Seria, Otdelenie Matematicheskii i Estestvennyka Nauk 7:793-800, 1934.
[E83] H. Edelsbrunner. A new approach to rectangle intersections. International Journal Computational Mathematics 13:209-219 and 221-229, 1983.
[GJPT78] M. R. Garey, D. S. Johnson, F. P. Preparata, and R. E. Tarjan. Triangulating a simple polygon. Information Processing Letters, 7:175-179, 1978.
[G72] R. L. Graham. An efficient algorithm for determining the convex hull of a finite planar set. Information Processing Letters, 1:132-133, 1972.
[GKS92] L. J. Guibas, D. E. Knuth, M. Sharir. Randomized incremental construction of Delaunay and Voronoi diagrams. Algorithmica 7:381-413, 1992.
[J73] R. A. Jarvis. On the identification of the convex hull of a finite set of points in the plane. Information Processing Letters, 2:18-21, 1973.
[KS86] D. Kirkpatrick and R. Seidel. The ultimate planar convex hull algorithm? SIAM J. Computing, 12:1:287-299, 1986.
[L77] C. L. Lawson. Software for C1 surface interpolation. Mathematical Software III, J. Rice ed., Academic Press, New York, 1977, 161-194.
[M85] E. M. McCreight. Priority search trees. SIAM Journal on Computing, 14:257-276, 1985.

Links
[TOPP] The Open Problems Project by Erik D. Demaine - Joseph S. B. Mitchell - Joseph O'Rourke
[OP] Open Problems by Jeff Erickson
[OPDCG] Open Problems on Discrete and Computational Geometry by Jorge Urrutia
[SP] Sample Computational Geometry Projects from McGill University

Animations