Course Scope
This course is an introductory course to Computational Geometry for undergraduate students. Computational Geometry is a study of algorithms and data structures for geometric objects. One important goal of this class is to make you become knowledgeable and comfortable enough to deal with any geometric problems. Common geometric problems can be found in many domains. Here are just a few examples:
- Robotics
- Computer Graphics
- Manufacturing (e.g., Computer Aided Design)
- Geographic information system (GIS, e.g., Google map)
Prerequisites
- CS310 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.
- Working knowledge of C/C++ for most computational geometry libraries are implemented in C/C++. Our textbook is called "Computational Geometry in C." However, you should be able to use Java for your projects.
Required Textbook
| Computational Geometry in C by Joseph O'Rourke
(Cambridge University Press; 2008 edition, ISBN # 978-3-540-77973-5) 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.
Recommended: Computational Geometry: Algorithms and Applications by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Cheong, third revised edition, Springer-Verlag, 2008. ISBN # 978-3-540-77973-5. You should be able to view the entire textbook from a GMU IP address. (This book is not required for this course.) Recently, O'Rourke also re-published his 1987 book, "Art Gallery Theorems and Algorithms" online, for free! |
Grading (tentative)
- Assignments 50%: There will be homework assignments, and programming assignments.
- Quizzes/Mid term Exam 20%
- Course project 30%
List of Topics (tentative)
- Triangulations
- Polygon Partitioning
- Intersection and Proximity problems
- Convex hull
- Range searching
- Point location
- Voronoi Diagrams and Delaunay Triangulations
- Robot Motion planning
- Quadtree/Octree
Policies (tentative)
All required assignments should be completed by the stated due date and time. The total score of your assignment score will be 10 points less every extra day after the due date (i.e., the 100 total points will become zero after 10 days pass the due date).
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.
The quizzes and exams will be a closed book exam - no notes will be allowed. There will be no makeups for the quizzes and exams.