|
|
CS633 is an introductory course to Computational Geometry.
Computational Geometry is a study of algorithms and data structures for geometric objects.
One important goal of CS633 is to make you become knowledgeable and comfortable
enough to deal with any geometric problems.
Prerequisite: CS583 or instructor's approval, which means
you should know sorting algorithms, graph algorithms, and basic data structures (lists, trees, graphs), and
know how to design and analyze the complexity of algorithms.
|
|
Required Textbook: Computational Geometry: Algorithms and Applications by
Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf, second revised edition, Springer-Verlag, 2000. ISBN # 3-540-65620-0.
Computational Geometry in C
by Joseph O'Rourke (Cambridge University Press; 2000 edition, ISBN # 0-521-64976-5) is also a useful book.
It seems that you can preview part of this book on google. As far as I know you should be able to get a copy of this book from the university bookstore.
(This book is not required for this course.)
In addition, we will study papers from various journals and conferences; these will be made available electronically.
|
Weekly Schedule, Readings, Assignments, Notes.
| Date | Lecture Notes |
Scope | Assignments |
Aug 30 | Introduction pdf |
Chapter 1 | See the lecture note |
Sep 06 | Line segment intersection pdf |
Chapter 2 | Exercise 2.1, 2.13 |
Sep 13 | Polygon triangulation pdf |
Chapter 3 | Exercise 3.13 and Programming Assignment 1: the Art Gallery Problem |
Sep 20 | Linear programming pdf |
Chapter 4 | no assignment |
Sep 27 | Range search pdf |
Chapter 5 | Exercise 5.10 |
Oct 04 | Point location pdf |
Chapter 6 | |
Oct 11 | Probabilistic motion planning pdf |
papers | Proposal presentations & Programming Assignment 2: Motion Planning |
Oct 18 | Voronoi diagrams pdf |
Chapter 7 | |
Oct 25 | Arrangement and duality pdf |
Chapter 8 | Paper review assignment |
Nov 01 | class canceled |
| |
Nov 08 | Delaunay triangulation pdf |
Chapter 9 | Exercise 9.11 |
Nov 15 | Convex hulls/Binary space partitions pdf |
Chapter 11,12 | |
Nov 22 | Thanksgiving |
| |
Nov 29 | Motion planning/Visibility graph pdf |
Chapter 13,15 | TBA |
Dec 06 | Project presentations |
| |
Dec 13 | Project presentations |
| Project report due |
Projects new!
1s CG Contest new!
Related websites (More information will be added)
Scope: In this course, we will learn about the following topics:
- Line segment intersection
- Convex hull
- Triangulations
- Proximity problems
- Range searching
- Point location
- Voronoi Diagrams
- Delaunay Triangulations
- Arrangements and Duality
- Binary space partitions
- Robot Motion planning
- Quadtree/Octree
- Visibility Graph
|
(Shortest geodesic paths, created by Jason Cantarella.
Stanford bunny created by
Greg Turk and Marc Levoy)
|
Applications:
Computational Geometry deals with many fundamental problems and many exciting applications in the following areas:
- Computer Graphics and Solid Modeling
- Robotics and Motion Planning
- Biological Applications
- Geographic Information System
- Manufacturing and prototype design
- Pattern Recognition
- Linear Programming
- Compression and Coding
- ...
Grading
- Quizzes or CS culture assignments
(please use this form) 5%
- Assignments 75%: There will be homework assignments, programming assignments, and paper review assignments.
- Project presentations (proposal and final) 10%
- Final project report 10%
- Bonus: Contests, seminar presentations, etc
Policies
All required assignments must be completed by the stated due date and time.
Your assignment score will be halved every extra day after the due date.
The quiz will be a closed book exam - no notes will be allowed.
You can also have an opportunity of making up one your missed/failed quiz by turning in
a CS culture assignment. A CS culture assignment is a one-page written summary
of a talk (please use this form to complete your assignment)
from a CS seminar (see http://cs.gmu.edu/~jmlien/seminar/) that you attend during the Fall'07 semester.
Please note that all coursework is to be done independently.
Plagiarizing the homework will be penalized by maximum
negative credit and cheating on the exam will earn you an F in the course.
See the GMU Honor Code System and Policies at
this page and
this page.
You are encouraged to discuss the material BEFORE you do the assignment.
As a part of the interaction you can
discuss a meaning of the question or possible ways of approaching the solution.
The homework should be written strictly
by yourself. In case your solution is based on the important idea of someone else
please acknowledge that in your solution, to avoid any accusations.
|
