CS 6170 - Computational Topology

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 (Reed graphs, Morse-Smale complexes, etc...). Special emphasis will be given to the analysis of their computation algorithms with respect to: (i) asymptotic complexity, (ii) robustness, and (iii) data structures and implementation issues. 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, mesh generation, data analysis, and scientific visualization.