Spring 1998

Ileana Streinu

- Reading and understanding of a Computational Geometry problem.
- Bibliography search.
- Contribution.

- An oral presentation: in class, last week of classes.
- A written presentation: an HTML page.
- Other: Java applet, model, etc. (if applicable: see below).

- JOR for J. O'Rourke's "Art Gallery Theorems and Algorithms.
- MMMO for M. de Berg etc. "Computational Geometry".
- GO for J.E. Goodman and J. O'Rourke, Handbook of Computational Geometry.

Nr |
Topic |
Reference |
Contribution |
Student |

JOR + bibliography search | problems for orthogonal objects | |||

JOR + bibliography search | problems for special shapes | |||

paper of Bjorling-Sachs + Souvaine + bibliography search | problem: conditions for 3 coloring of a polygon with one hole (k holes); bibliography search. | |||

MMMO Ch. 10 Windowing, with a bit of Ch. 5 for Range trees. Bibliography search minimal. | Understanding of material: quite a lot! | |||

MMMO Ch 12. Bibl. search minimal. | Understanding of material: quite a lot! | |||

MMMO Ch. 13 and 15. | Java implementation of "naive" algorithm for computing vis. graphs. | |||

Handout (2 pages from a book by Giblin), paper of de Fraysseyx, Pach and Pollack and bibl. search (graph drawing bibliography). | Understanding of material: quite a lot! Bibliography search. | |||

JOR | Physical and computer models (Mathematica?) of the two main polyhedra in the book illustrating the issues. | |||

Your references. Can start from GO, for instance. | To be discussed thoroughly with Ileana | Robot Arm Motion Reversing linkages Stabbing information for a polygon |

- Reading and understanding of material. The presentation
should include:
- Definition of the motivating problem.
- Main result(s) and/or data structure(s).
- Proof/algorithm.
- Contribution.

- Bibliography search.
- Identifying related problems and papers using Geombib, the Graph Drawing bibliography or other bibliography search tools.
- Finding 2-3 papers in the library; reading introduction; figuring out what are their main contributions and how they relate to the original problem.
- Writting a short (less than one page) summary of results found in these extra references, and giving a full list of references to related problems/papers.

- Contribution:

Acceptable contributions are:- Java implementation of a simple algorithm related to the topic.
- Thinking about an open problem related to the topic of the reading, and presenting coherent approaches towards its resolution: experimentation with cases, examples, formulating a conjecture, working towards it or towards connter-examples, etc. A final solution may not be found, so the process of "thinking" about it should be documented carefully.
- A 3d model, and a computer model (using, for example, Mathematica) of an interesting example (this is for topic 8, mainly).
- Figuring out a result presented in a paper (as opposed to a book).
- Figuring out a more complex set of results from a book.
- Other: to be decided by discussing with Ileana.

Last modified March 26, 1998.