CS 497 JE, Spring 2000 Computational Geometry TuTh 11:00-12:15, 159 Altgeld Hall Instructor: Jeff Erickson http://www.uiuc.edu/~jeffe/cs497/

Computational geometry is the field of theoretical computer science devoted to the design, analysis, and implementation of algorithms and data structures to solve geometric problems. These problems arise in several different areas, including computer graphics, robotics, databases, data mining, parallel computing, statistics, and pure math. Their solutions combine traditional algorithmic techniques with beautiful results from combinatorics, geometry, and other mathematical areas. Computational geometry was the breeding ground for several important techniques that later spread to the broader algorithms community - for example, dynamic data structures, randomized algorithms, and external memory computing - and continues to be one of the most active, interesting, and applicable areas of algorithms research today.

Topics:

The exact topics will depend on the interests of the participants, but here is a sample of possibilities. Please let me know if there's something specific you want to talk about!

Objects: Polygons Convex polytopes Triangulations Voronoi diagrams Convex decompositions Arrangements Visibility graphs

Problems: Convex hulls Nearest neighbors Point location Range searching LP-type problems Intersection Lower bounds

Techniques/Paradigms: Sweep Divide and conquer Prune and search Random sampling Dynamization Kinetic data structures Perturbation

Applications: Mesh generation Simplification Reconstruction Motion planning Collision detection Hidden surface removal Clustering

Administrivia

• Course announcement: PostScript or PDF
• UI Direct call number: 01698
• Credit: 1 unit
• Prerequisite: CS 373 or equivalent, or my permission.
  Mathematically and/or algorithmically mature undergraduates are welcome!!
• Recommended Textbooks:
  • Computational Geometry: Algorithms and Applications by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf (Springer-Verlag, 2nd edition, 2000). Available February 1.
  • Computational Geometry in C by Joseph O'Rourke (Cambridge University Press, 2nd edition, 1998).
  • I'll also distribute recent conference and journal papers in class and/or on the course web site.

Some useful web pages:

• My Computational Geometry Pages
• Nina Amenta's Directory of Computational Geometry Software
• David Eppstein's Geometry in Action and Geometry Junkyard
• Search the Geometry Literature Database, thanks to René van Oostrum

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I talk in pictures not in words. - Peter Gabriel "...And Through the Wire" Peter Gabriel III (Melt) (1980) I have no arguments to offer, my figures are my proofs. Laugh away these truths and facts if you can. - Theodore Heisel The Circle Squared Beyond Refutation (1934) Automatic polygon meter Analog toy computer item Triangulate me, moot copy Goatee community portal Oatmeal recomputing toy Optional gutter may come Typical rommmate tongue Get your calm emotion, Pat. Get your campmate lotion Immature galoot potency A triplet comet among you Cut lame emotion - go party! Operate coital Tommy-gun Copulate my rotation gem. Young male potato metric Go try tapioca emolument Ugly poetic monotremata Magical poem torn out yet Automatic mangle poetry - Anagrams of "computational geometry" found at OneAcross.com

CS 497 (Spring 2000) - Jeff Erickson (jeffe@cs.uiuc.edu) 09 Jan 2000