Computational Topology with Applications
Class Information:
|
Term |
Number (index) |
Subject |
Catalog # |
Section |
Days |
Time |
Location |
Office Hours |
|
Spring 2011 |
16246 |
CS |
6967 |
0001 |
Tuesday, Thursday |
12:25 PM-01:45 PM |
MEB 3105 |
TBD |
Course Overview. This course provides a gentle introduction to topology-based techniques for the analysis and visualization of geometric models. Students will learn about fundamental topological invariants (connectedness, Euler characteristic, orientability, etc…) and constructs (Reeb graphs, Morse-Smale complexes, etc…), as well as efficient algorithms for their computation. Special emphasis will be given to the analysis of the algorithms with respect to: (i) asymptotic complexity, (ii) robustness, and (iii) data structures and implementation issues. The practical use of the techniques presented in class will be demonstrated for the analysis of geometric models commonly used in Computer Graphics and Scientific Visualization. Successful completion of the course will enable the students to pursue new research directions in this field and/or apply the most recent topological techniques to related areas such as computer graphics, geometric modeling, meshing, data analysis, and scientific visualization.
Prerequisites. There are no formal prerequisites for this class. Students will be expected to have basic knowledge of geometric data structures and algorithmic techniques.
Tentative Syllabus (changes based on student feedback will be
considered):
Reading and supplemental material
There is no formal book for class. The instructor will distribute printouts of notes or research papers related to each lecture.
The following links include various relevant materials such as book, research papers, and software:
· Books:
o Topology (2nd Edition) by J. Munkres
o Morse Theory by J. Milnor
o Combinatorial Topology by P. S. Alexandrov
o An Introduction to Morse Theory by Y. Matsumoto
· Other links:
o Computational Geometry Pages by J. Erickson
o GemDir by E. Mücke
o CGAL
Assignments
The students will be given individual and group assignments. The main assignment will be a project. Although the students will be provided with a list of available projects, the students are encouraged to propose projects in areas of personal interest. For larger projects the students will be allowed to work in small groups.
Late Submission of Assignments
Assignments will not be accepted late. Students will be given a one-time two-day extension for an unexpected event.
Class Participation and Absences
Participation in class is an
integral part of the course. Attendance is mandatory.
More than two unjustified absences will impact negatively the grade.
Grading
Each student will be evaluated based on:
· Attendance and participation in class (20%),
· Assignments (20%),
· Project (50%),
· Final project presentation (10%).
Students With Disabilities
The University of Utah seeks to provide equal access to its programs, services and activities for people with disabilities. If you will need accommodations in the class, reasonable prior notice needs to be given to the Center for Disability Services, 162 Olpin Union Building, 581-5020 (V/TDD). CDS will work with you and the instructor to make arrangements for accommodations.
All written information in this course can be made available in alternative format with prior notification to the Center for Disability Services.