CSC274b
Spring 2000
Ileana Streinu

Final Project

Thursday, March 9, 2000

Requirements

The project work has three components:
  1. Reading and understanding of a Computational Geometry problem.
  2. Bibliography search.
  3. Contribution.
The final presentation has at least the first two components from the list below:
  1. An oral presentation: in class, last week of classes.
  2. A written presentation: an HTML page.
  3. Other: Java applet, C++/LEDA program, model, etc. (if applicable: see below).

Project Topics

You can choose one of the following, or suggest another topic - in which case you have to come up with a coherent plan of what you want to do, including a bibliographic starting point (book chapter, paper). The references are to books on reserve in the Science Library. Abbreviations: The papers and other materials (such as a short proof from a book) will be handed in by Ileana, if you choose that topic.
Nr
Topic
Reference
Contribution
Student
1
Art Gallery Theorems for Orthogonal polygons
JOR + bibliography search problems for orthogonal objects
2
Art Gallery Theorems for Special Shape Polygons: star, monotone, etc.
JOR + bibliography search problems for special shapes
Reading a paper
Ellen
3
Art Gallery Theorems for polygons with holes
paper of Bjorling-Sachs + Souvaine + bibliography search problem: conditions for 3 coloring of a polygon with one hole (k holes); bibliography search.
4
Geometric Data Structures: interval trees, segment trees, range trees.
MMMO Ch. 10 Windowing, with a bit of Ch. 5 for Range trees. Bibliography search minimal. Understanding of material
5
Robot Motion Planning and Visibility Graphs.
MMMO Ch. 13 and 15. Understanding of material. Mark Overmars software.
Veronica
Naomi
6
Visibility Graphs.
MMMO Ch. 13 and 15, for motivation. Java implementation of "naive" algorithm for computing vis. graphs.
Read, understand a paper.
Beenish
7
Planar graphs: straight line embeddings.
Handout (2 pages from a book by Giblin). Perhaps additional references, if needed. (paper of de Fraysseyx, Pach and Pollack and bibl. search, graph drawing bibliography). Understanding of material. Use of applets available on the web. Bibliography search. Use of Graph Drawing resources. Graph Server

8
Art Gallery Theorems in 3d
JOR Physical and computer models (Mathematica, GeomView) of the two main polyhedra in the book illustrating the issues.

9
Problems with 3d polytopes: folding, unfolding. Strange unfoldings
Komei Fukuda Understanding the problem. Material available on web page. Physical and computer models (Mathematica, GeomView).
Courtney
10
Problems with linkages
Erik Demaine , Godfried Toussaint Understanding the problem. Material available on web page. Physical and computer models (Mathematica, GeomView).
Tracy
11
Geometric software
CGAL

Installation of software; understanding the demos; understand and present 1-2 geometric algorithms; reading paper(s) about CGAL and understanding the project and using the library.
Elif
12
Your topic, if related to a current project, or of particular interest for you. Look at some nice open problems from Jeff Erickson's page.
Your references. Can start from GO, for instance. To be discussed thoroughly with Ileana
Jesse, collison detection for Asteroids game.

Expected Work

  1. Reading and understanding of material. The presentation should include:
  2. Bibliography search.
  3. Contribution:
    Acceptable contributions are:

Last modified March 26, 1998.