AMS 545/ CSE 555 Course Material, Spring 2013

Joe Mitchell, Math Tower 1-109, 632-8366

The course meets Tues/Thurs 2:30pm-3:50pm in Psychology A 137.

All ARE Welcome!


Office Hours for Joe: Tues (1:00-2:00), Wed (2:30-3:30), or by appointment, or drop by whenever (don't be shy!)
Teaching Assistants: Thanh Dang (office hours Mondays, 1:40 - 3:40 PM in Harriman 010), dangngocthanh1989 "AT" yahoo.com; Kan Huang (office hours Tuesday 10am-11am, Wednesdays 4-5pm, in Math 2-109, starting Feb 26), khuang@ams.sunysb.edu

Announcements:

Final exam is in Psychology A 137 (usual classroom), Tuesday, May 21, 11:15-1:45

Updated Quiz/hw schedule: Quiz4 will be Thurs, April 25 (postponed 1 week), and hw6 will be due the same day (4/25). Quiz5/hw7 remains as scheduled previously (May 2).

I added the remark (4/15/13) to problem 5 of hw6 that in a simple arrangement of planes in 3D, each pair of planes must intersect in a line (ie, no 2 planes is parallel).

I added a nondegeneracy assumption to problem 1, hw6 (4/10/13). See below.

Tentative schedule for remaining quizes: Quiz 4 on April 18, Quiz 5 on May 2.

Main Course Information

Course Information (AMS 545/CSE 555, Spring 2013) This is the main course information sheet with details about exams, homeworks, grading, etc. Homework solutions will be posted on Blackboard.
Lots of information about what computational geometry is all about can be found at Jeff Erickson's Geometry Page.

Homeworks and Other Handouts


See Blackboard for a growing list of possible (optional) projects.
Some SAMPLE PROJECTS, done by previous students: randomized incremental CH (java); point location search in trapezoidal diagram (Visual C++).

The introductory class on Tuesday, January 29 (Powerpoint slides are available on Blackboard) will give an overview of what computational geometry is and what types of problems we study in the course. I will include some demos, which are applets linked from the slides and linked below.

Homework 1, due Thursday, Feb 14 in class.
Solution posted on Blackboard after due date.
Notes on Melkman's Algorithm
An example of the Bentley-Ottmann sweep
A description of Melkman's algorithm (the applet link no longer works)
link to T. Chan's paper on output sensitive convex hull computation. See also the convex hull algorithms notes of Robert Pless (based on David Mount's course notes on CG)

Homework 2, due Thursday, Feb 28 in class.
Solution posted on Blackboard after due date.

Homework 3, due Tuesday, Mar 12 in class.
Solution posted on Blackboard after due date.

Homework 4, due Thursday, Mar 28 in class.
Solution posted on Blackboard after due date.

An example of the construction of the Kirkpatrick hierarchy

VoroGlide, Voronoi diagram demo
Cool demo of Fortune's sweep algorithm for Voronoi diagrams
Handout on Voronoi/Delaunay notes (updated 3/28/13)

Homework 5, due Thursday, Apr 4 in class.
Solution posted on Blackboard after due date.

Homework 6 (updated 4/10, just problem 1; updated 4/14, fixing typo in problem 3; updated 4/15 to add remark in problem 5), due Thursday, Apr 18 in class (postponed to Thurs, April 25)
Solution posted on Blackboard after due date.

Example using Davenport-Schinzel argument, for complexity of a single face in an arrangement of rays

Homework 7, due Thursday, May 2 in class.
Solution posted on Blackboard after due date.

Algorithmic Motion Planning, by Micha Sharir

Practice final exam; solutions

Another Practice final exam Solution is posted on Blackboard.

Miscellaneous Links of Relevance:

  • Required textbook, by de Berg, Cheong, van Kreveld, and Overmars (3rd Edition).
  • Recommended textbook by O'Rourke, entitled "Computational Geometry in C, 2nd Edition"
  • Computational Geometry at Stony Brook
  • Tom Fevens course notes, slides and links, following our text
  • CG Tutorial, with applets
  • Geometry software, part of geometryalgorithms.com
  • Godfried Toussaint's CG page where Godfried keeps many useful links to cool stuff in CG
  • G. Aloupis. A history of linear-time convex hull algorithms for simple polygons.
  • Graph drawing slides, Dynamic CG slides, Brown University
  • Convex hull algorithm applets, with cool Java applets for Graham's scan, Jarvis' march, and Quick hull
  • Duality Viewer Applet, for seeing things in primal/dual planes
  • A description of Melkman's algorithm (the applet link no longer works)
  • link to T. Chan's paper on output sensitive convex hull computation. See also the convex hull algorithms notes of Robert Pless (based on
  • David Mount's course notes on CG
  • On the Hertel-Mehlhorn algorithm to compute a decomposition of a simple polygon into convex polygons
  • shortest path in simple polygon, with horizontal trapezoidization, triangulation, "random" simple (monotone) polygon; by Josh Tyler
  • Search the geom.bib, Barcelona search engine
  • The Open Problems Project (TOPP), with J. O'Rourke and E. Demaine
  • NYU Geometry Seminars
  • Computational Geometry on the WWW, Maintained by Guilherme Albuquerque Pinto
  • David Eppstein's Geometry in Action
  • Jeff Erickson's Geometry Page
  • David Eppstein's General Geometric References
  • Mesh Generation Pages
  • Voronoi.com, page of Chris Gold
  • CGAL, the Computational Geometry Algorithms Library
  • Directory of Computational Geometry Software
  • QuickCD, Stony Brook's fast collision detection code (my work with J. Klosowski, M. Held)