Course Info

• Instructor: Hamid Zarrabi-Zadeh
• Course Syllabus
• Quera Page (Assignments, Announcements)

Lectures

• Introduction
• Sample Geometric Problems [BCKO Ch1]
• Polygons, Primitive Operations [O Ch1.3, 7.4]
• Convex Hulls
• Convex Hull Algorithms in 2D [BCKO Ch1]
• Lower Bounds, Ben-Or's Theorem [Ben-Or's Paper]
• Output-Sensitive Algorithms for Convex Hull [Chan's PhD Thesis]
• Geometric Duality
• Duality and Its Applications, Lower/Upper Envelopes [BCKO Ch8.2], [O Ch6.5]
• 3D Convex Hulls
• Convex Hulls in 3D, Properties and Representation [O Ch4.1, 4.4], [BCKO Ch2.2]
• Algorithms for 3D Convex Hulls, Convex Hulls in Higher-d [BCKO Ch11.2-3], [O Ch4]
• Line Segment Intersection and Arrangement
• Line Segment Intersection, Plane Sweep, Divide & Conquer [BCKO Ch2], [Balaban's Paper]
• Arrangement of Lines, Applications, k-Levels [BCKO Ch8], [O Ch6.1-3]
• Voronoi Diagrams and Delaunay Triangulations
• Voronoi Diagrams, Properties, Fortune's Algorithm [BCKO Ch7.1-2]
• Delaunay Triangulations, Connection to CH, A Randomized Algorithm [BCKO Ch9], [O Ch5.7]
• Applications of Voronoi Diagrams and Delaunay Triangulations [O Ch5.5]
• Higher-Order Voronoi Diagrams, Smallest-Width Annulus [BCKO Ch7.3-4], [O Ch6.6]
• Linear Programming
• Linear Programming: Definition and Applications [BCKO Ch4.1-2]
• Solging LP in Low Dimentiond, Megiddo's Algorithm [Megiddo's Paper]
• Seidel's Randomized Algorithm, Smallest Enclosing Circle [BCKO Ch4.3-7]
• Point Location
• A Randomized Incremental Algorithm [BCKO Ch6]
• The Prune and Search Algorithm of Kirkpatrick[Kirkpatrick's Paper]
• Polygon Triangulation
• Trapezoidal Method, Seidel's Algorithm [BCKO Ch3], [Seidel's Paper]
• Applications of Triangulation, Art Gallery Problem [BCKO Ch3.1]
• Range Searching
• K-D Trees, Range Trees, Fractional Cascading [BCKO Ch5]
• Interval Trees, Segment Trees, Priority Search Trees [BCKO Ch10]

References

• [BCKO] M. de Berg, O. Cheong, M. van Kreveld, and M. Overmars. Computational Geometry: Algorithms and Applications. 3rd Edition, Springer-Verlag, 2008.
• [O] J. O'Rourke. Computational Geometry in C. 2nd Edition, Cambridge University Press, 1998.